



Class 

Book-_—- 


l^gUUGUr DSPOSm 










HEATH’S 


LOGARITHMIC 

AND 

TRIGONOMETRIC TABLES 


WITH AN INTRODUCTION BASED 
ON CURTISS AND 310 CL TO NS TRIG0N03IETRY 


BY 


EARNEST JACKSON OGLESBY 

A) 

PROFESSOR OF MATHEMATICS 
NEW YORK UNIVERSITY 



D. C. HEATH AND COMPANY 

BOSTON NEW YORK CHICAGO LONDON 

ATLANTA SAN FRANCISCO DALLAS 


)« 



QAss 


Copyright, 1927, 

By D. C. Heath and Company 

2 J 7 


©Cl A 1010222 

PRINTED IN U.S.A. 


N0V-7'2f 


CONTENTS 


Oo 

r» 


i 


' 

£ 


PAGE 

Introduction to Tables.. 


FOUR-PLACE TABLES 

Table I. Squares of Numbers. 2 

Table II. Values of Functions and Radians ... 4 

Table III. Logarithms of Numbers. 10 

Table IV. Logarithms of Functions. 12 


FIVE-PLACE TABLES 

Logarithms of the Trigonometric Functions 


Table Va. Auxiliary Table of S and T . . . .21 

Table V6. Angles Near 0° and 90°.22 

Table VI. Logarithms of Functions . . . .25 

Table VII. Common Logarithms of Numbers ... 73 

Table VIII. Constants with Their Logarithms . . 93 

Table IX. Natural Logarithms of Numbers ... 94 




INTRODUCTION 


1 . Definition of the logarithm of a number. If a number 
N is expressed as a power of 10 , 

N = 10", 

then the exponent, x, is called the logarithm of N (to the base 10); 
in symbols we write, 

log N = X. 

Thus by definition 

= N. 

More generally, if 

a" = N, 

then X is the logarithm of N to the base a, and we write 
log„ N = X. 

Thus by definition 

aiosaN = jsl. 

For computational purposes the base 10 is most con¬ 
venient. For theoretical purposes in higher mathematics 
a base called e, where 

e = 2.71828 •••, 

is simplest to use. Logarithms to the base 10 are called 
common logarithms; to the base e natural logarithms. 
Except when otherwise indicated the base is understood to 
be 10. 

No power of 10 yields a negative number; hence negative 
numbers do not have logarithms. 

2 . Exponents. From the definition of logarithm given 
above it is seen that logarithms are exponents. We therefore 
shall find it profitable to review briefly the general laws of 
exponents. 


11 


TRIGONOMETRY 


We shall assume that the base a is positive; the exponents 
m and n are any real numbers. 


(1) 

a^ • a” 



(2) 

a^ 

= a^-n = 

. 1 

a” 

fjn-m 

(3) 

(^m)n 

= a”*”. 


(4) 

0/ 

1 cf 

II 

is a positive integer). 

(5) 

V 

aJ 

11 

II 

(</ay. 

(6) 

a-” 

_ 

a” 


(7) 

ao 

= 1. 



3. Fundamental laws of logarithms. 

I. The logarithm of the product of two numbers equals the 
sum of the logarithms of the factors. That is, 

(1) log MN = log M + log N, 

II. The logarithm of the quotient of two numbers equals the 
logarithm of the dividend minus the logarithm of the divisor. 
Symbolically, 

(2) V " ^ ~ 

III. The logarithm of the nth power of a number equals n 
times the logarithm of the number. That is, 

(3) log M" = n log M. 

IV. The logarithm of the rth root of a number is one rth 
of the logarithm of the number. In symbols, 

(4) log VM = I log M. 

r 

The proofs of these theorems are as follows: 

By definition 

M = jy- ^ 

TCf log — 

MN = 10'°= and ^ = 10 


INTRODUCTION 


iii 


By the first law of exponents, 
MN = 10^°®^ • 


Therefore 


2Qlog M+logiV 

log MN = log M + log N, 


which is Law I. 

Similarly, by the second law of exponents, 

M ^ 

N 

Therefore 

M 


2Qlog M—log 


log — = log ilf - log N, 


which is Law II. 

By the third law of exponents. 


M^ = XQnlogM^ 

Hence 

log = n log M, 

which is Law III. 

The fourth law follows from the third since 

__ 1 

</M = M\ 

For we have 

_ I 1 

log VM = log = - log M. 

r 

Note. The preceding laws are true whatever base of logarithms 
is- used. To prove them for a base a, we simply replace 10 by a 
throughout the argument. 


4. Characteristic and mantissa. As examples of loga¬ 
rithms, we may write the following pairs of equivalent state¬ 
ments : 


10 = lOb 

log 10 = 1 

100 = 102, 

log 100 = 2 

1000 = 103, 

log 1000 = 3 

1 = 100, 

log 1=0 

.1 = 10-1, 

log .1 = - 

.01 = 10-2, 

log .01 = — 


IV 


TRIGONOMETRY 


The logarithms of the numbers 10, 100, 1000, ••• are the 
positive integers 1, 2, 3, •••; the logarithm of 1 is 0; and the 
logarithms of .1, .01, .001, ••• are the negative integers — 1, 
— 2, — 3, •••. The logarithm of any other positive number 
can be expressed as the sum of an integral part and a positive 
decimal part. The integral part is called the characteristic, 
the decimal part the mantissa of the logarithm of the number. 
For example, in Table VII (p. 73) we find 

log 25 = 1.39794. 

The characteristic is 1 and the mantissa .39794. 

Again 

log5 = 0.69897. 


The characteristic is 0 and the mantissa .69897. 

The logarithm of any number between 1 and 10 lies 
between log 1 and log 10, that is, between 0 and 1. Hence, 
the characteristic of the logarithm of any number between 1 
and 10 is 0. 

To get a general rule for the characteristic let us consider 
the following examples: 

50 = 10 • 5, log 50 = log 10 + log 5 = 1.69897; 

500 = 100 • 5, log 500 = log 100 + log 5 = 2.69897; 

.5 = .1-5, log.5=log.l +log5 =-1 +0.69897; 
.05 = .01 • 5, log .05 = log .01 + log 5 = - 2 + 0.69897. 

By units’ place in a number we mean the first place to the 
left of the decimal point when the number is written in 
decimal notation. Thus for each of the numbers 4.2, 34, 
and 604.71, the digit 4 is in units’ place. 

Suppose now that, for a given number N, in going from 
the first significant figure to units’ place we move K places 
to the right; then the number can be expressed as 10^V', 
where V' is a number between 1 and 10. Thus, 500 = 10^ • 5. 
Hence 

log N = log 10^ + log N' = K log N '; 
and the characteristic of log N is K, 


INTRODUCTION 


V 


Suppose next that in going from the first significant figure 
of N to units’ place we move K places to the left; then the 
number can be expressed as where N' is between 

1 and 10. Thus, .05 = lO-^ • 5. Hence 

log N = log 10~^ + log N' = — K log N' 
and the characteristic of log N is — K. 

Rule. To find the characteristic of log N, first find how far 
it is from the first significant figure of N to units’ place. If 
it is 

K places to the right, the characteristic is K. 

K places to the left, the characteristic is — K. 

Thus the characteristic of log 9.3 is 0; of log 93,000,000 
is 7; of log .123 is — 1; and of log .000005 is — 6. 

From the preceding paragraphs we see that the mantissa 
of log N is log N', where N' is the number between 1 and 10 
which is obtained from N by merely shifting the decimal 
point to the proper place. Hence the mantissa depends 
only on the succession of digits in N, and not at all on the 
position of the decimal point. Accordingly the decimal 
point may be ignored when one looks for the mantissa. The 
mantissa is found from a table of logarithms as explained 
in the descriptions of Tables HI and VII. 

When the characteristic is negative, care must be taken 
in writing the logarithm. Thus it would be a mistake to 
write 

log .05 = - 2.69897, 

for the number in the right member equals — 2 — .69897 and 
not the correct value — 2 + .69897. One commonly used 
way of writing the logarithm is 2.69897, it being understood 
that only the characteristic is affected by the negative sign. 
Another method is to use such relations as 
- 2 = 8 - 10 = 18 - 20 

and write 

log .05 = 8.69897 - 10 = 18.69897 - 20. 


VI 


TRIGONOMETRY 


We shall adopt the latter system, in which the negative 
characteristic is expressed as a positive integer minus a 
multiple of 10. 

Note. If another base of logarithms than 10 were used, we would 
not have such simple rules for finding characteristic and mantissa. 
It is because of this relative simplicity that the base 10 is generally 
used in computations. 


Table I. Squares of Numbers 


5. Squares of numbers. This table gives the approximate 
values of the squares of numbers from 1.00 to 9.99. Its 
use is illustrated in the following examples. 

Examples. — 1. To find (5.92)^. 

On page 3, go down the column headed N to 5.9, then across to 
the column headed 2. The approximate value required is found to 
be 35.05. 


2. To find (5.925)2. 

We interpolate with the aid of the adjacent table (it should 
be done mentally after a little 
practice) and obtain the correc¬ 
tion, 

X = 5/10 X 11 = 5.5 = 6 10 ” L5.925 -J 11 

approximately. We then have 
the approximation, 

(5.925)2 = 35.05 + .06 = 35.11. 



N 

W2 


r r5.92o 

35.05"| 

10 

15.925 

5.930 

-J 

35.16 


3. To find (59.25)2. 

We have 

59.25 = 10 X 5.925; 

(59.25)2 = 102 X (5.925)2 = 100 X 35.11, from Example 2, 
= 3511. 

Similarly, 

(592.5)2 = 1002 X (5.925)2 = 351,100; 

(.5925)2 = .3511; 

(.05925)2 = .003511. 






INTRODUCTION 


vii 


It should now be clear how the approximate value of the 
square of any number whatever is found. We may formulate 
the rule: For a given number, shift the decimal point to the 
right {or left) k places to obtain a number between 1 and 10. 
Find the square of this from the Table. Shift the decimal 
point iri this result 2 k places to the left (or right) to get the 
required square. 


6. Square roots. The square root of a number n in 
the interior of Table I is given by the corresponding number 
N read off from the left of the row and the top of the column 
in which n lies. We may, therefore, use the Table of Squares 
for the extraction of square roots. 


We note that the interior numbers lie between 1 and 100. We 
get the square roots of numbers in this range directly, though inter¬ 
polation may be needed. Thus 

V3.496 = 1.870, V34.96 = 5.912. 


A number which does not lie between 1 and 100 can be expressed 
as the product of such a number by a power of 10 whose square root 
is simple. Thus 


349.6 = 100 X 3.496, 
3496. = 100 X 34.96, 
34960. = 10000 X 3.496, 

Hence 

V349.6 =V'l0d XV3.496, 
= 10 X 1.870, 

= 18.70, 

V34%. = 59.12, 

V34960. = 187.0. 


.3496 = .01 X 34.96, 
.03496 = .01 X 3.496, 
.003496 = .0001 X 34.96. 


V.3496 =V .01 xv'34.96, 
= .1 X 5.912, 

= .5912, 

V.03496 = .1870, 

V.003496 = .05912. 


It should now be clear how the approximate square root 
of any number whatever can be found by use of the Table. 
A rule may be formulated as follows: For a given number 
shift the decimal point an even number of places^ say 2 k, to 
the right {or left) to get a number between 1 and 100. Find the 










Vlll 


TRIGONOMETRY 


square root of this number from the Tables. In this square 
root shift the decimal 'point k places to the left {or right) to get 
the required number. 

Table II. Four-Place Values of Functions and Radians 

7. Angles 10' apart are given from 0° up to 45° in the first 
column of pages 4-8, and from 90° down to 45° in the last 
column. The values of the functions are given in successive 
columns. For angles given at the left, we read the name of 
the function at the top of the columns; for angles at the 
right, we read the functions at the bottom of the columns. 

Examples. — 1. To find sin 4° 40'. 

We look on page 4, go down the left-hand column headed “De¬ 
grees’’ to 4° 40' and across to the column headed “Sin” ; the entry 
is 814, which means that sin 4° 40' = .0814, the first digit, in this 
case 0, being given only at intervals in this table. 

2. To find cot 14° 10'. 

We turn to page 5, go down the first column to 14° 10', across to 
the column headed “Cot ” and read 3.962. Thus cot 14° 10' = 3.962. 

3. To find cos 66° 20'. 

We turn to page 6, go up the last column to 66° 20', across to 
the column with “Cos” at the bottom, and read .4014. That is, 
cos 66° 20' = .4014. 

4. Given that tan A =.7954, to find A. 

Look down the column headed “Tan” to entry .7954; go across 
to the first column and find A = 38° 30'. 

8 . Interpolation. In finding the value of a function of 
an angle, such as 17° 23', which is not given in the Table 
but lies between two angles that appear, we use the 
method of interpolation, as illustrated in Examples 1 and 
2 below. In Examples 3 and 4 the method is applied in 
finding the angle when the value of one of its functions is 
given. 


INTRODUCTION 


IX 


Examples. — 1. To find sin 17° 23'. 

The given angle, 17° 23', is three-tenths of the way from 17° 20' 
to 17° 30'. We assume that sin 17° 23' is three-tenths of the way 
from sin 17° 20' to sin 17° 30'. The sine of 17° 23' will then be 
obtained by taking 3/10 of the amount by which sin 17° 30' exceeds 
sin 17° 20', and adding this correction to sin 17° 20'. Hence 
sin 17° 23' = sin 17° 20' + 3/10 (sin 17° 30' - sin 17° 20') 

= .2979 + 3/10 (.0028) = .2979 -h .00084 
= .2987 approximately. 

Since the Tables give values to only four places, we give only four 
places in our value of sin 17° 23'. This amounts to calling the 
correction .0008 instead of .00084. We would have used .0008 for 
any correction greater than .00075 and less than .00085. It is 
customary to disregard the decimal point in the tabulated values 
and call the tabular difference 28 instead of .0028, and the correction 
8 instead of .0008. 

Another way to explain the preceding interpolation is to state 
that we have assumed that when an angle increases, its sine increases 
proportionally; or, in other words, that differences between angles 
are proportional to differences between their sines. For the ex¬ 
amples just solved the accompanying small table indicates these 
differences. We thus have 


X _ 3 

Angle 

Sin 

^ ~ 10* 

■ „ ri7° 20' 

.2979“! 

Then ic = 8.4 = 8 approximately; jq 

117° 23' 

-J 

and 

17° 30' 

.3007 

sin 17° 23' = .2979 -f .0008 




= .2987. 


The assumption just made that differences between angles are 
proportional to differences between the values of a function of those 
angles is not exactly true, but it gives rise to errors which are negli¬ 
gible when the differences involved are small. 


2. To find cot 17° 15'. 


Angle 

Cot 

From the little table at the right 


■ ri7° 10' 

3.2371 

we have 

10 

Li7° 15' 

-J 

X = 5/10 X 33 = 16.5. 


17° 20' 

3.204 


\ 


33 










X 


TRIGONOMETRY 


\ 

The correction x could be called either 16 or 17. In all such cases 
we shall arbitrarily use the even numbers; here we take a- = 16. 
We note that the cotangent decreases when we go from 17° 10' to 
17° 20'; hence the correction, which should take us 5/10 of the way 
from cot 17° 10' to cot 17° 20', must be subtracted from the former. 
We have 

cot 17° 15' = 3.237 - .016 = 3.221. 

3. Given tan A = .4361, to find A. 

We find that the angle A lies between 23° 30' and 23° 40', as 
shown to the right. By the prin- 


ciple of proportional differences 
we have 

Angle 

Tan 

r r23°30' 

.43481 

X = ||xl0 = ^ = 3.7. 10 

4 A 

.436lJ 

35 35 

23° 40' 

.4383 

Hence 



A = 23° 30' + 4' 

= 23° 34'. 


4. Given cos A = .4100, to find A. 


Proceeding as before we have 

Angle 

Cos 

a: = X 10 = 8. 

r r65°40' 

X 

.41201 

26 10 

L A 

.4100J 

Hence 

65° 50' 

.4094 


A =.65° 48'. 


9. Conversion Table. In the second column of each 
page of Table II will be found the radian equivalent of the 
degrees and minutes in the first column. By the use of this 
Table, with interpolation, we can convert the measure of an 
angle from degrees and minutes into radians with four-place 
accuracy; and vice versa we can change four-place radian 
measure into degrees and minutes. 

Example. — Express 20° 23' in radians. 

20° 20' = .3549 radians 
20° 30' = .3578 radians 

For 20° 23' the correction which should be added to .3549 would 
be tV X 29 = 9, giving .3558 radians. 











INTRODUCTION 


XI 


Table III. Four-Place Logarithms of Numbers 

10. Finding logarithms from a table. In this table the 
mantissas are given correct to four decimal places for the 
integers from 100 to 999. The direct use of the table is 
illustrated in the following examples. 

Examples. — I. To find log 320 to four places. 

From the rule we find that the characteristic is 2. For the 
mantissa turn to Table III. We go down the column headed N 
to the number 32, across the row to the column headed 0 and find 
5051. When the decimal point, which is omitted in the Table for 
simplicity in printing, is placed ahead of the first 5, this is the man¬ 
tissa. Hence 

log 320 = 2.5051 to four places. 

2. To find log 325 to four places. 

In this case go across in the row 32 to the column headed 5 and 
find 119. The first figure of log 320 which occurs at the beginning 
of the row 32 in column 0 is understood to precede this, so that 
the mantissa is .5119; hence 

log 325 = 2.5119. 

3. To find log .507 to four places. 

To go from the first significant figure, 5, to units’ place we move 
one place to the left; hence the characteristic is — 1. In Table III 
in row 50 go across to column 7, and find *050; this is not to be 
preceded by the first figure, 6, in log 500; the * calls attention to 
a change, and we are to take the first figure, 7, of logarithms in the 
next row. Thus the mantissa is .7050, and we have 
log .507 = 9.7050 - 10. 


4. To find log .06378 to four places. 


We may form the little table to the 

N 

log W 

right by reference to Table III. The 

637 

8041 

required logarithm is .8 of the way from 

637.8 


log 637 toward log 638. Hence we must 
add .8 of the difference 8048 — 8041 as 

638 

8048 


a correction to 8041; the correction is therefore .8X7 = 5.6 = 6 
approximately. The same correction could be found in the mar- 


TRIGONOMETRY 


xii 

ginal table on the right in row 63 and column 8. We add the 
correction and put in the decimal point to get the mantissa. The 
characteristic being — 2, we have the result 

log .06378 = 8.8047 - 10. 

11. Finding a number whose logarithm is given. If the 

logarithm of a number is given and the number is required, 
the steps of the preceding section are reversed, as illustrated 
in the following examples. 

Examples. — 1. Given log N = 1.9258, to find N. 

We look in the four-place logarithm table for the mantissa .9258. 
On page 11 we find the corresponding number 8430, the final zero 
indicating that no interpolation is necessary and that the number 
differs from 8430 by very little — less than 1. Since the charac¬ 
teristic is 1, units’ place is one place to the right of the first significant 
figure. Hence 

N = 84.30. 

2. Given log N = 5.5011, to find N. 

The mantissa .5011 is found in row 31 and column 7; it corre¬ 
sponds to the number 3170. Since the characteristic is 5, units’ 
place is 5 places to the right of the 3. Hence 

N = 317000 to four significant figures. 

3. Given log N = 8.8080 — 10, to find N. 

The mantissa .8080 lies between two tabulated values, 8075 and 


8082, and hence we interpolate. 



The given mantissa is 5/7 of the 

N 

log W 

way from the first to the second of 

r r 6420 

8075-] 

these values in the Tables. The 10 


8080J 

difference of the corresponding 

6430 

8082 


numbers 6420 and 6430 in the 

Tables is 10. Hence we add the correction x = 5/7 X 10 = 7 
to 6420 and get 6427. Since the characteristic is — 2, units’ place 
is two places to the left of the 6. Hence N = .06427. 

Instead of interpolating as we did, we could use the marginal 
table under Prop. Pts. on the right (p. 11). The difference 5 between 




INTRODUCTION 


xiii 

the value 8075 in the Table and the given value 8080 is found in 
the row 64 in both columns 7 and 8 of this marginal table. Under 
the agreement to make the correction even when we have a choice, 
we take 8 as the fourth digit, and this is to be placed after the 
number 642 which corresponds to the mantissa 8075, giving 6428. 
Hence N = .06428. 

The values of N found by the methods of the two preceding para¬ 
graphs differ by a unit in the last place. 

Table IV. Four-Place Logarithms of Functions 

12. Logarithms of functions. Table IV, pages 12-17, gives 
four-place logarithms of the functions at intervals of 10'. 
For angles from 0° to 45°, which are found in the first column, 
we read the functions at the top of other columns; for angles 
from 45° to 90°, found in the last column, we read the func¬ 
tions at the bottom. The third column, which is headed d 1', 
gives the change in the logarithm of the sine (L Sin) for a 
change of 1' in the angle; this aids in interpolations. The 
fifth column, headed cd 1', shows the common difference of 
the logarithms of the tangent and the cotangent for a change 
of 1' in the angle. The next to last column gives the cor¬ 
responding difference for the logarithm of the cosine. 

The characteristic which is printed in the Table must 
be decreased by 10, the — 10 having been omitted for sim¬ 
plicity of printing. 

Examples. — 1. To find log sin 23° 52' to four places. 

On page 15 of the Tables we go down the first column to 23° 50', 
across to the column headed L Sin, and read 9.6065. Since the 
difference for 1' between angles 23° 50' and 24° 00' is 2.8, the cor¬ 
rection for 2' is 2 X 2.8 = 6 approximately. And since the L Sin 
increases when the angle increases we add the correction. Hence 
log sin 23° 52' = 9.6071 - 10. 

2. To find log tan 52° 18' to four places. 

On page 17 of the Tables we find 52° 10' in the last column; we go 
across to the column having L Tan at the bottom, and read 10.1098. 


XIV 


TRIGONOMETRY 


The difference for 1' between 52° 10' and 52° 20' is 2.6. Hence 
the correction for 8' is 8 X 2.6 = 21 approximately. Since L Tan 
increases when the angle increases from 52° 10' to 52° 20', we add 
the correction. The final result is 

log tan 52° 18' = 10.1119 - 10 = 0.1119. 

3. To find log cos 71° 33' to four places. 

On page 14 we find 71° 30' in the last column. Going across to the 
column having L Cos at the bottom we read 9.5015. The difference 
for 1' is 3.8 and hence for 3' it is 3 X 3.8 = 11 approximately. 
Since L Cos decreases when the angle increases from 71° 30' to 
71° 40' we subtract the correction. The final result is 
log cos 71° 33' = 9.5004 - 10. 

4. To find the acute angle A, given 

log cot A = 8.9843 — 10. 

On page 13 in the column having L Cot at the bottom, we find 
8.9966 and 8.9836. Hence A lies between the corresponding angles 
84° 20' and 84° 30'. The difference in the logarithms is (disre¬ 
garding the decimal point) 9966 — 9843 = 123; since the difference 
for 1' is 13.0, the correction to the angle is 123/13.0 = 9'. Hence 
A = 84° 29'. 

Table V 

13. Angles near 0° or 90°. A glance at Table VI shows 
that for small angles, from 0° to 2° or further, the differences 
in log sin, log tan, and log cot are large. It follows that 
interpolation will not be very accurate. The same remark 
applies for angles from 90° to 88° or further, for log cos, 
log tan, and log cot. On the other hand the differences are 
so small for log cos when angles are near zero that when the 
function is given, the angle is not well determined. For 
example, log cos A = 9.99997 — 10 for all angles from 0° 37' 
to 0° 43'. On this account, when a small angle is to be 
found it is desirable to use a formula, if possible, which will 
give the sine, tangent, or cotangent of the angle. Similarly, 


INTRODUCTION 


XV 


to determine an angle near 90° we should avoid a formula 
which gives its sine, but use one giving its cosine or tangent. 

To increase the accuracy of interpolation for angles near 
0° or 90° we use the special Table V6 (pages 22-24). This 
gives the values of log sin for angles at intervals of 10" 
from 0° to 3°. For angles from 0° to 3° we can find the 
values of log cos and log tan from the formulas 

log cos A = 10 — C — 10, 
log tan A = log sin A + C, 

where C is a correction which is given in the Table. This 
formula givee an error of at most 1 in the last figure of the 
mantissa. For an angle from 87° to 90° use the cofunction 
of the complementary angle. 

Examples. — 1. To find log tan 0° 37' 43" by use of 
Table Yh. 

We find 

log tan 0° 37' 40" = 8.03970 - 10, 
log tan 0° 37' 50" = 8.04162 - 10. 

The difference for 10" is 192; the correction for 3" is 
3/10 X 192 = 57.6 = 58 approximately. 

Hence log tan 0° 37' 43" = 8.04028 - 10. 

2. To find B, given log tan B = 2.26170. 

The angle is near 90°. Let A be its complement, A = 90° — B. 
Then 

log cot A = 2.26170. 

Hence 

log tan A = 10 — log cot A — 10 
= 7.73830 - 10. 

From Table Yb, 

log tan 0° 18' 40" = 7.73480 - 10, 
log tan 0° 18' 50" = 7.73866 - 10. 

By interpolation we find 

A = 0° 18' 49.07". 

Hence 

B = 89° 41' 10.93". 


XVI 


TRIGONOMETRY 


14. Interpolation by Table Va. Interpolation in Tables 
\b or VI may be avoided and higher accuracy attained 
by use of Table Ya. 

3. To find log tan 0° 37' 43" by means of Table Va. 

We have the formula log tan A = log A' + T, where A' is the 
number of minutes in the angle; here A' = 37.717. Then, by 
Table VII, 

log A' = 1.57654 

and by Table Ya 

T = 6.46374 - 10. 

Hence 

log tan 0° 37' 43" = 8.04028 - 10. 

4. To find A if log tan A = 2.26170, by Table Ya. 

The angle is near 90°. We are therefore to use the formula 
log cot M = Ti + log Ai', where T/ = 90° — A expressed in minutes. 
We have 

log cot A = 7.73830 — 10. 

From Table VI, A = 89° 41' approximately. Hence Ai = 19' 
approximately. From Table Ya 

Ti = 6.46373 - 10. 

Since 

log Ai = log cot A — Ti 

we have 

log Ml' = 1.27457. 

From Table VII 

Ml' = 18.818'. 

Hence 

Ml = 18'49.08", 

M = 90° - Ml = 89° 4T 10.92". 

Table VI. Five-Place Logarithms of Functions 

15. Five-place logarithms of functions. Table VI is a 
five-place table of the logarithms of functions, with angles 
given at intervals of I'. On each page the number of degrees 
in the angle is read at the top or bottom, the number of min¬ 
utes at the left or right; interpolation is necessary for parts 
of a minute. The angles 0° to 44° are found at the tops of 
the pages, 89° to 45° at the bottoms. 


INTRODUCTION 


XVll 


Examples. — 1. To find log sin and log cot of the angle 
23° 41'37". 

On page 50, which has 23° printed at the top, we find 
log sin 23° 41' = 9.60388, log sin 23° 42' = 9.60417. 

The required log sin lies between these two, whose difference is 29 
(see third column), the decimal point in the values of log sin being 
disregarded for simplicity in carrying out the interpolation. Since 
1' = 60", the correction for 37" is 37/60 of 29. This may be found 
by use of the Prop. Pts. tables. In the column headed 29 we find 
the correction for 30" to be 14.5, and for 7" to be 3.4; thus the 
total correction is 14.5 + 3.4 = 18. Since log sin increases as the 
angle increases from 23° 41' to 23° 42' the correction is added. 
Thus we find 

log sin 23° 41' 37" = 9.60406 - 10. 

Similarly the correction for log cot is 17.0 + 4.0 = 21. Since 
log cot decreases the correction is subtracted, and we get 
log cot 23° 41' 37" = 10.35770 - 10. 

2. To find log tan and log cos of the angle 54° 57' 42". 

On page 62, which has 54° at the bottom, we enter the column 

having log tan at the bottom, go up to the row having 57 in the last 
column, and find 

log tan 54° 57' = 10.15397. 

To interpolate, we note that the difference of successive values of 
log tan is 27. The correction for 40" is 18.0; for 2" it is 1/10 of 
that for 20"; thus for 42" it is 18.0 + 0.9 = 19. Since log tan 
increases when the angle increases, this is added and we get 
log tan 54° 57'42" = 10.15416 - 10. 

Similarly the correction for log cos is 12.0 + 0.6 = 13; since 
log cos decreases, we have 

log cos 54° 57' 42" = 9.75900 - 10. 

3. To find the acute angle A, given 

log cos A = 8.77990 — 10. 

On page 28, in the column having L Cos at the bottom 8.78152 
and 8.77943 correspond to angles 86° 32' and 86° 33'. Hence A 
lies between these angles. The difference 78152 — 77990 = 162; 


TRIGONOMETRY 


xviii 


the tabular difference in the third column is 209. Hence the correc¬ 
tion to the angle 86° 32' is 162/209 of 60". In the Prop. Pts. tables 
we find in the column headed 209 in the 40" row 139.3; the differ¬ 
ence 162 — 139.3 = 22.7 is nearly equal to the number in the 7" row. 
Hence the correction is about 47". 

A = 86° 32' 47". 


Table VH. Five-Place Logarithms of Numbers 
16. Five-place logarithms of numbers. In this table 
on page 73 the logarithms are given correct to five decimal 
places for the integers from 1 to 100. Beginning on page 74 
the mantissas are given correct to five decimal places for 
the integers from 1000 to 10009. The following examples 
illustrate the use of the table. 


Examples. — 1. Given log N = 9.58065 — 10, to find N. 

We look in the five-place table for the mantissa .58065. We find 
on page 79 that it lies between two 
tabulated values, 58058 and 58070, 
being 7/12 of the way from the 
former to the latter. The desired 
number is 7/12 of the way from 
38070 to 38080: the correction is 
a: = 7/12 X 10 = 6, and thus we 

get 38076. Since the characteristic is — 1, the decimal point pre¬ 
cedes the 3, and we have 

N = .38076. 



N 

log N 


r r38070 

58058“| 

10 


580654 


38080 

58070 


12 


The interpolation could have been accomplished by use of the 
Prop. Pts. table in the margin on page 79. The tabular difference 
is 58070 — 58058 = 12; the partial difference is 58065 — 58058 = 7. 
In the Prop. Pts. column headed 12, we find a number as near 7 as 
possible; it is 7.2; this occurs in row 6, which gives the correction. 
The interpolation should be done mentally. 

2. To find log 4680 to five places. 

Turn to Table VII (p. 81). In column N go down to row 468 and 
in column 0 find 67025. The decimal point is to be placed before 
the 6 to give the mantissa. Since the characteristic is 3, we have 
log 4680 = 3.67025. 




INTRODUCTION 


XIX 


3. To find log .4691 to five places. 

On page 81 in row 469 and column 1 we find 127. This is to be 
preceded by the first two digits 67 of log 4680, giving 67127. Since 
the characteristic is — 1, we have the result 

log .4691 = 9.67127 - 10. 

4. To find log .04679 to five places. 

On page 81, in row 467 and column 9 we find *015. If it were not 
for the *, we would place the two digits 66 of column 0 before these 
three, but the * indicates a change to 67 which occurs in the follow¬ 
ing row. The characteristic being — 2, we have 

log .04679 = 8.67015 - 10. 

5. To find log 15897 to five places. 

From page 75 of the Tables we form the little table shown to the 
right. We must interpolate. The re¬ 
quired logarithm is .7 of the way from N log N 

20112 to 20140. Hence we must add to 1589.0 20112 

the former the correction found by taking 1589.7 

.7 of the difference 20140 - 20112 = 28, 1590.0 20140 

that is, .7 X 28 = 19.6 = 20 approxi¬ 
mately. This correction could be found by looking in the Prop. Pts. 
table on the margin of page 75, in the Table, in column 28 and row 7, 
where we find 19.6. The interpolated value of log N is therefore 
20112 + 20 = 20132. Putting in the decimal point, and observing 
that the characteristic is 4, we have 

log 15897 = 4.20132. 

Examples showing the use of Tables III and VII 

17. Products and quotients found by use of logarithms. 

We are now ready to use the fundamental laws of logarithms 
(§ 3) in computations. To compute a product we find the 
logarithms of the factors, add them to get the logarithm of 
the product, then find in a table the number of which that 
is the logarithm. 


XX 


TRIGONOMETRY 


Examples. — 1. To find N — 3.728 X .006378 by use of 
four-place logarithms. 

log 3.728 = 0.5714 
log .006378 = 7.8047 - 10 
log N = 8.3761 - 10 
N = .02378. 


To compute a quotient we use Law II (§ 3). We find 
the logarithms of the numerator and denominator, and 
subtract the latter from the former, getting the logarithm of 
the quotient. The number of which this is the logarithm is 
found in the Tables; it is the required quotient. 

2. To find N = by use of a four-place table of 

3697 

logarithms. 


The characteristic of log 42.73 is written as 11 — 10 so that the 
subtraction will be possible without use of a negative sign except 
with the — 10. 

log 42.73 = 11.6307 - 10 
log 3697 = 3.5678 
log N = 8.0629 - 10 
N = .01156. 

o rp 1 .38275 X .048293 , r o i 

* = :062191 X 8346.8 ^ 

table of logarithms. 


Calling the numerator N and the denominator D, we carry out 


the computation as follows : 

log .38275 = 9.58292 - 10 
log .048293 = 8.68389 - 10 
log N = 18.26681 - 20 
log D = 12.71525 - 10 
log a; = 5.55156 - 10 


log .062191 = 8.79373 - 10 
log 8346.8 = 3.92152 

log D = 12.71525 - 10 

a: = .000035609 


18. Cologarithms. Division may be carried out in a 
slightly different way. Instead of subtracting the logarithm 
of the denominator, we may add the negative of that loga- 









INTRODUCTION 


XXI 


rithm. When the latter is written so that the decimal part 
is positive it is called the cologarithm of the number. Thus 
colog N = — log N, 
and the law for division becomes 

log ~ = log M + colog N. 

The following examples will show how the cologarithm is 
found. 

Examples. — 1. To find colog 376.4 to four places. 

We find log 376.4 = 2.5757. We get the cologarithm by adding 
the negative of this to 10.0000 — 10: 

10.0000 - 10 
- log 376.4 = - 2.5757 
colog 376.4 = 7.4243 - 10 

2. To find colog .006259 to five places. 

10.00000 - 10 
- log .006259 = - 7.79650 + 10 
colog .006259 = 2.20350 

It is seen that the cologarithm may be found by starting at 
the left of the logarithm and subtracting each digit from 9 
until we come to the last which is different from zero; this 
one is subtracted from 10 and the subsequent digits of the 
cologarithm are 0. Using this rule it is easy to write down 
the cologarithm directly from the Table, care being taken to 
include the characteristic. This work must be done mentally 
if cologarithms are to be used to advantage. 

Example 3 of the preceding section would be solved by use 
of cologarithms as follows : 

log .38275 = 9.58292 - 10 
log .048293 = 8.68389 - 10 
colog .062191 = 1.20627 
colog 8346.8 = 6.07848 - 10 
log X = 25.55156 — 30 
X = .000035609 





TRIGONOMETRY 


xxii 


19. Powers and roots. The third law of logarithms 
(§3) enables us to find a power of a number. We take 
the logarithm of the number, multiply it by the exponent, 
getting the logarithm of the power, and find the number 
corresponding to that logarithm. 


Example. — To find x = (.3728)^ 

Using a four-place table we have 

log .3728 = 9.5714 - 10; 
multiplying by 5 gives 

log a: = 47.8570 - 50, 
a: = .007194. 


The student should also solve this problem by use of five-place 
tables and obtain 


a: = .0072012. 


The fourth law of logarithms (§3) is used in extracting 
roots. To find the rth root of a number, take the logarithm 
of the number, divide it by r to obtain the logarithm of the 
rth root, and find the corresponding number. 


Example. — To find V.3728; •v^.3728. 
Using five-place tables we have 

log .3728 = 19.57148 - 20; 


dividing by 2 gives 

log V.3728' = 9.78574 - 10, 
V.3728 = .61057. 


Also 


log .3728 = 29.57148 - 30; 

dividing by 3 gives 

log V.3728 = 9.85716 - 10, 
V.3728 = .71972. 


We wrote the negative characteristic in each problem in such a 
way that after the division the only negative part of the logarithm 
was — 10. 








INTRODUCTION xxiii 


20. Computations involving negative numbers. We have 
remarked that negative numbers do not have logarithms. 
To obtain a product or quotient involving negative numbers, 
we may find the numerical value by disregarding the signs, 
then subsequently prefix the proper sign to the result. If 
there was an even number of negative factors, the sign 
should be +, if an odd number it should be —. 


Table VIII. Constants with Their Logarithms 

21. Logarithms of constants. This table gives, on page 
88, the values of a number of important constants which 
enter into trigonometric computations, together with the 
logarithms of these constants. No explanation of this 
table is necessary. 


Table IX. Natural Logarithms of Numbers 

22. Change of base of logarithms. In a note at the 
end of § 4, we remarked that bases of logarithms other than 
10 may be used. How can we find the logarithm of a num¬ 
ber N to a base b, if its logarithm to a base a is known? 
We may arrive at the answer as follows: 

By definition 


Take the logarithm of each number to the base a, using the 
third law of logarithms, § 3, to simplify the left member. 
We find that 


Hence 


log6 N • loga h = loga N. 


log6 N = 


log« N 

loga h ’ 


which answers our question. 

If in this formula we substitute N = 
loga a = 1, we have 

_1 _ 

loga h 


a, and observe that 


logb a = 




XXIV 


TRIGONOMETRY 


Hence the preceding formula is equivalent to 
logb N = loga N • log6 a. 

If we take a = 10, h = e, where e is the base of natural 
logarithms (§ 1 ), we have the most important special case, 


\oge N = 


\ogioN ^ log 10 iV 
logio e .43429 


2.3026 logio N. 


23. Explanation of Table. Table IX gives the natural 
logarithms of numbers from 1.00 to 10.09 correct to five 
places of decimals. The note at the top of page 94 explains 
how to find the logarithm of a number which does not come 
within the range of this table. The laws for finding the 
characteristic as given for base 10 do not hold for this table. 

Examples. — 1. Find the value of loge 4.06 to five places. 

On page 94, in row 4.0 and column 6 we find *0118. The * in¬ 
dicates a change in the first two digits of the logarithm from 1.3 to 
1.4 so that we have 

\oge 4.06 = 1.40118. 

2. Find the value of loge 406 to five places. 

Since 406 does not come within the range of our table, it is neces¬ 
sary for us to shift the decimal point until we get a number which 
does occur in the table. We note that 
406 = 102.4.06. 

Hence log* 406 = loge 10^ -f loge 4.06. 

= 2 loge 10 H- loge 4.06 
= 2(2.30259)-!- 1.40118 
loge 406 = 6.00636. 

Interpolation in Table IX is carried out exactly as in 
Tables III and VII. 

It should be noted that Table IX is also a table of exponen¬ 
tials. For by the definition of logarithms as given in § 1 




INTRODUCTION 


XXV 


so that we can find the value of e-^ by using 

X = lOgeN 

and finding N from the Table. 

Example. — Find the value of g^-^ons 
Here logeiV = 1.40118. From the Table 

N = 4.06, 

so that 

el-40118 = 4 06 . 



#•> 




FOUR-PLACE TABLES 


2 


SQUARES OF NUMBERS 


I 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.0 

1.000 

1.020 

1.040 

1.061 

1.082 

1.103 

1.124 

1.145 

1.166 

1.188 

1.1 

1.210 

1.232 

1.254 

1.277 

1.300 

1.323 

1.346 

1.369 

1.392 

1.416 

1.2 

1.440 

1.464 

1.488 

1.513 

1.538 

1.563 

1.588 

1.613 

1.638 

1.664 

1.3 

1.690 

1.716 

1.742 

1.769 

1.796 

1.823 

1.850 

1.877 

1.904 

1.932 

1.4 

1.960 

1.988 

2.016 

2.045 

2.074 

2.103 

2.132 

2.161 

2.190 

2.220 

1.5 

2.250 

2.280 

2.310 

2.341 

2.372 

2.403 

2.434 

2.465 

2.496 

2.528 

1.6 

2.560 

2.592 

2.624 

2.657 

2.690 

2.723 

2.756 

2.789 

2.822 

2.856 

1.7 

2.890 

2.924 

2.958 

2.993 

3.028 

3.063 

3.098 

3.133 

3.168 

3.204 

1.8 

3.240 

3.276 

3.312 

3.349 

3.386 

3.423 

3.460 

3.497 

3.534 

3.572 

1.9 

3.610 

3.648 

3.686 

3.725 

3.764 

3.803 

3.842 

3.881 

3.920 

3.960 

2.0 

4.000 

4.040 

4.080 

4.121 

4.162 

4.203 

4.244 

4.285 

4.326 

4.368 

2.1 

4.410 

4.452 

4.494 

4.537 

4.580 

4.623 

4.666 

4.709 

4.752 

4.796 

2.2 

4.840 

4.884 

4.928 

4.973 

5.018 

5.063 

5.108 

5.153 

5.198 

5.244 

2.3 

5.290 

5.336 

5.382 

5.429 

5.476 

5.523 

5.570 

5.617 

5.664 

5.712 

2.4 

5.760 

5.808 

5.856 

5.905 

5.954 

6.003 

6.052 

6.101 

6.150 

6.200 

2.5 

6.250 

6.300 

6.350 

6.401 

6.452 

6.503 

6.554 

6.605 

6.656 

6.708 

2.6 

6.760 

6.812 

6.864 

6.917 

6.970 

7.023 

7.076 

7.129 

7.182 

7.236 

2.7 

7.290 

7.344 

7.398 

7.453 

7.508 

7.563 

7.618 

7.673 

7.728 

7.784 

2.8 

7.840 

7.896 

7.952 

8.009 

8.066 

8.123 

8.180 

8.237 

8.294 

8.352 

2.9 

8.410 

8.468 

8.526 

8.585 

8.644 

8.703 

8.762 

8.821 

8.880 

8.940 

3.0 

9.000 

9.060 

9.120 

9.181 

9.242 

9.303 

9.364 

9.425 

9.486 

9.548 

3.1 

9.610 

9.672 

9.734 

9.797 

9.860 

9.923 

9.986 

10.05 

10.11 

10.18 

3.2 

10.24 

10.30 

10.37 

10.43 

10.50 

10.56 

10.63 

10.69 

10.76 

10.82 

3.3 

10.89 

10.96 

11.02 

11.09 

11.16 

11.22 

11.29 

11.36 

11.42 

11.49 

3.4 

11.56 

11.63 

11.70 

11.76 

11.83 

11.90 

11.97 

12.04 

12.11 

12.18 

3.5 

12.25 

12.32 

12.39 

12.46 

12.53 

12.60 

12.67 

12.74 

12.82 

12.89 

3.6 

12.96 

13.03 

13.10 

13.18 

13.25 

13.32 

13.40 

13.47 

13.54 

13.62 

3.7 

13.69 

13.76 

13.84 

13.91 

13.99 

14.06 

14.14 

14.21 

14.29 

14.36 

3.8 

14.44 

14.52 

14.59 

14.67 

14.75 

14.82 

14.90 

14.98 

15.05 

15.13 

3.9 

15.21 

15.29 

15.37 

15.44 

15.52 

15.60 

15.68 

15.76 

15.84 

15.92 

4.0 

16.00 

16.08 

16.16 

16.24 

16.32 

16.40 

16.48 

16.56 

16.65 

16.73 

4.1 

16.81 

16.89 

16.97 

17.06 

17.14 

17.22 

17.31 

17.39 

17.47 

17.56 

4.2 

17.64 

17.72 

17.81 

17.89 

17.98 

18.06 

18.15 

18.23 

18.32 

18.40 

4.3 

18.49 

18.58 

18.66 

18.75 

18.84 

18.92 

19.01 

19.10 

19.18 

19.27 

4.4 

19.36 

19.45 

19.54 

19.62 

19.71 

19.80 

19.89 

19.98 

20.07 

20.16 

4.5 

20.25 

20.34 

20.43 

20.52 

20.61 

20.70 

20.79 

20.88 

20.98 

21.07 

4.6 

21.16 

21.25 

21.34 

21.44 

21.53 

21.62 

21.72 

21.81 

21.90 

22.00 

4.7 

22.09 

22.18 

22.28 

22.37 

22.47 

22.56 

22.66 

22.75 

22.85 

22.94 

4.8 

23.04 

23.14 

23.23 

23.33 

23.43 

23.52 

23.62 

23.72 

23.81 

23.91 

4.9 

24.01 

24.11 

24.21 

24.30 

24.40 

24.50 

24.60 

24.70 

24.80 

24.90 

5.0 

25.00 

25.10 

25.20 

25.30 

25.40 

25.50 

25.60 

25.70 

25.81 

25.91 

5.1 

26.01 

26.11 

26.21 

26.32 

26.42 

26.52 

26.63 

26.73 

26.83 

26.94 

5.2 

27.04 

27.14 

27.25 

27.35 

27.46 

27.56 

27.67 

27.77 

27.88 

27.98 

5.3 

28.09 

28.20 

28.30 

28.41 

28.52 

28.62 

28.73 

28.84 

28.94 

29.05 

5.4 

29.16 

29.27 

29.38 

29.48 

29.59 

29.70 

29.81 

29.92 

30.03 

30.14 









































































































I 


SQUARES OF NUMBERS 


3 


N 

0 

1 

1 

2 

3 

4 1 

1 

5 

6 

7 

8 

9 

5.5 

30.25 

30.36 

30.47 

30.58 

30.69 

30.80 

30.91 

31.02 

31.14 

31.25 

5.6 

31.36 

31.47 

31.58 

31.70 

31.81 

31.92 

32.04 

32.15 

32.26 

32.38 

5.7 

32.49 

32.60 

32.72 

32.83 

32.95 

33.06 

33.18 

33.29 

33.41 

33.52 

5.8 

33.64 

33.76 

33.87 

33.99 

34.11 

34.22 

34.34 

34.46 

34.57 

34.69 

5.9 

34.81 

34.93 

35.05 

35.16 

35.28 

35.40 

35.52 

35.64 

35.76 

35.88 

6.0 

36.00 

36.12 

36.24 

36.36 

36.48 

36.60 

36.72 

36.84 

36.97 

37.09 

6.1 

37.21 

37.33 

37.45 

37.58 

37.70 

37.82 

37.95 

38.07 

38.19 

38.32 

6.2 

38.44 

38.56 

38.69 

38.81 

38.94 

39.06 

39.19 

39.31 

39.44 

39.56 

6.3 

39.69 

39.82 

39.94 

40.07 

40.20 

40.32 

40.45 

40.58 

40.70 

40.83 

6.4 

40.96 

41.09 

41.22 

41.34 

41.47 

41.60 

41.73 

41.86 

41.99 

42.12 

6.5 

42.25 

42.38 

42.51 

42.64 

42.77 

42.90 

43.03 

43.16 

43.30 

43.43 

6.6 

43.56 

43.69 

43.82 

43.96 

44.09 

44.22 

44.36 

44.49 

44.62 

44.76 

6.7 

44.89 

45.02 

45.16 

45.29 

45.43 

45.56 

45.70 

45.83 

45.97 

46.10 

6.8 

46.24 

46.38 

46.51 

46.65 

46.79 

46.92 

47.06 

47.20 

47.33 

47.47 

6.9 

47.61 

47.75 

47.89 

48.02 

48.16 

48.30 

48.44 

48.58 

48.72 

48.86 

7.0 

49.00 

49.14 

49.28 

49.42 

49.56 

49.70 

49.84 

49.98 

50.13 

50.27 

7.1 

50.41 

50.55 

50.69 

50.84 

50.98 

51.12 

51.27 

51.41 

51.55 

51.70 

7.2 

51.84 

51.98 

52.13 

52.27 

52.42 

52.56 

52.71 

52.85 

53.00 

53.14 

7.3 

53.29 

53.44 

53.58 

53.73 

53.88 

54.02 

54.17 

54.32 

54.46 

54.61 

7.4 

54.76 

54.91 

55.06 

55.20 

55.35 

55.50 

55.65 

55.80 

55.95 

56.10 

7.5 

. 56.25 

56.40 

56.55 

56.70 

56.85 

57.00 

57.15 

57.30 

57.46 

57.61 

7.6 

57.76 

57.91 

58.06 

58.22 

58.37 

58.52 

58.68 

58.83 

58.98 

59.14 

7.7 

59.29 

59.44 

59.60 

59.75 

59.91 

60.06 

60.22 

60.37 

60.53 

60.68 

7.8 

60.84 

61.00 

61.15 

61.31 

61.47 

61.62 

61.78 

61.94 

62.09 

62.25 

7.9 

62.41 

62.57 

62.73 

62.88 

63.04 

63.20 

63.36 

63.52 

63.68 

63.84 

8.0 

64.00 

64.16 

64.32 

64.48 

64.64 

64.80 

64.96 

65.12 

65.29 

65.45 

8.1 

65.61 

65.77 

65.93 

66.10 

66.26 

66.42 

66.59 

66.75 

66.91 

67.08 

8.2 

67.24 

67.40 

67.57 

67.73 

67.90 

68.06 

68.23 

68.39 

68.56 

68.72 

8.3 

68.89 

69.06 

69.22 

69.39 

69.56 

69.72 

69.89 

70.06 

70.22 

70.39 

8.4 

70.56 

70.73 

70.90 

71.06 

7i.23 

71.40 

71.57 

71.74 

71.91 

72.08 

8.5 

72.25 

72.42 

72.59 

72.76 

72.93 

73.10 

73.27 

73.44 

73.62 

73.79 

8.6 

73.96 

74.13 

74.30 

74.48 

74.65 

74.82 

75.00 

75.17 

75.34 

75.52 

8.7 

75.69 

75.86 

76.04 

76.21 

76.39 

76.56 

76.74 

76.91 

77.08 

77.26 

8.8 

77.44 

77.62 

77.79 

77.97 

78.15 

78.32 

78.50 

78.68 

78.85 

79.03 

8.9 

79.21 

79.39 

79.57 

79.74 

79.92 

80.10 

80.28 

80.46 

80.64 

80.82 

9.0 

81.00 

81.18 

81.36 

81.54 

81.72 

81.90 

82.08 

82.26 

82.45 

82.63 

9.1 

82.81 

82.99 

83.17 

83.36 

83.54 

83.72 

83.91 

84.09 

84.27 

84.46 

9.2 

84.64 

84.82 

85.01 

85.19 

85.38 

85.56 

85.75 

85.93 

86.12 

86.30 

9.3 

86.49 

86.68 

86.86 

87.05 

87.24 

87.42 

87.61 

87.80 

87.98 

88.17 

9.4 

88.36 

88.55 

88.74 

88.92 

89.11 

89.30 

89.49 

89.68 

89.87 

90.06 

9 5 

90.25 

90.44 

90.63 

90.82 

91.01 

91.20 

91.39 

91.58 

91.78 

91.97 

9!6 

92.16 

92.35 

92.54 

92.74 

92.93 

93.12 

93.32 

93.51 

93.70 

93.90 

9.7 

94.09 

94.28 

94.48 

94.67 

94.87 

95.06 

95.26 

95.45 

95.65 

95.84 

9*8 

96.04 

96.24 

96.43 

96.63 

96.83 

97.02 

97.22 

97.42 

97.61 

97.81 

9.9 

98.01 

98.21 

98.41 

98.60 

98.80 

99.00 

99.20 

99.40 

99.60 

99.80 


































































































4 FOUR-PLACE VALUES OF FUNCTIONS AND RADIANS II 


Degrees 

Radians 

Sin 

Cos 

Tan 

Cot 

Sec 

Csc 



0° 00' 

.0000 

.0000 

1.0000 

.0000 


1.000 


1.5708 

90° 00' 

10 

029 

029 

000 

029 

343.8 

000 

343.8 

679 

50 

20 

058 

058 

000 

058 

171.9 

000 

171.9 

650 

40 

30 

.0087 

.0087 

1.0000 

.0087 

114.6 

1.000 

114.6 

1.5621 

30 

40 

116 

116 

.9999 

116 

85.94 

000 

85.95 

592 

20 

50 

145 

145 

999 

145 

68.75 

000 

68.76 

563 

10 

1° 00' 

.0175 

.0175 

.9998 

.0175 

57.29 

1.000 

57.30 

1.5533 

89° 00' 

10 

204 

204 

998 

204 

49.10 

000 

49.11 

504 

50 

20 

233 

233 

997 

233 

42.96 

000 

42.98 

475 

40 

30 

.0262 

.0262 

.9997 

.0262 

38.19 

1.000 

38.20 

1.5446 

30 

40 

291 

291 

996 

291 

34.37 

000 

34.38 

417 

20 

50 

320 

320 

995 

320 

31.24 

001 

31.26 

388 

10 

2° 00' 

.0349 

.0349 

.9994 

.0349 

28.64 

1.001 

28.65 

1.5359 

88° 00' 

10 

378 

378 

993 

378 

26.43 

001 

26.45 

330 

50 

20 

407 

407 

992 

407 

24.54 

001 

24.56 

301 

40 

30 

.0436 

.0436 

.9990 

.0437 

22.90 

1.001 

22.93 

1.5272 

30 

40 

465 

465 

989 

466 

21.47 

001 

21.49 

243 

20 

50 

495 

494 

988 

495 

20.21 

001 

20.23 

213 

10 

3° 00' 

.0524 

.0523 

.9986 

.0524 

19.08 

1.001 

19.11 

1.5184 

87° 00' 

10 

553 

552 

985 

553 

18.07 

002 

18.10 

155 

50 

20 

582 

581 

983 

582 

17.17 

002 

17.20 

126 

40 

30 

.0611 

.0610 

.9981 

.0612 

16.35 

1.002 

16.38 

1.5097 

30 

40 

640 

640 

980 

641 

15.60 

002 

15.64 

068 

20 

50 

669 

669 

978 

670 

14.92 

002 

14.96 

039 

10 

4° 00' 

.0698 

.0698 

.9976 

.0699 

14.30 

1.002 

14..34 

1.5010 

86° 00' 

10 

727 

727 

974 

729 

13.73 

003 

13.76 

981 

50 

20 

756 

756 

971 

758 

13.20 

003 

13.23 

952 

40 

30 

.0785 

.0785 

.9969 

.0787 

12.71 

1.003 

12.75 

1.4923 

30 

40 

814 

814 

967 

816 

12.25 

003 

12.29 

893 

20 

50 

844 

843 

964 

846 

11.83 

004 

11.87 

864 

10 

5° 00' 

.0873 

.0872 

.9962 

.0875 

11.43 

1.004 

11.47 

1.4835 

85° 00' 

10 

902 

901 

959 

904 

11.06 

004 

11.10 

806 

50 

20 

931 

929 

957 

934 

10.71 

004 

10.76 

777 

40 

30 

.0960 

.0958 

.9954 

.0963 

10.39 

1.005 

10.43 

1.4748 

30 

40 

989 

987 

951 

992 

10.08 

005 

10.13 

719 

20 

50 

.1018 

.1016 

948 

.1022 

9.788 

005 

9.839 

690 

10 

6° 00' 

.1047 

.1045 

.9945 

.1051 

9.514 

1.006 

9.567 

1.4661 

84° 00' 

10 

076 

074 

942 

080 

9.255 

006 

9.309 

632 

50 

20 

105 

103 

939 

no 

9.010 

006 

9.065 

603 

40 

30 

.1134 

.1132 

.9936 

.1139 

8.777 

1.006 

8.834 

1.4573 

30 

40 

164 

161 

932 

169 

8.556 

007 

8.614 

544 

20 

50 

193 

190 

929 

198 

8.345 

007 

8.405 

515 

10 

7° 00' 

.1222 

.1219 

.9925 

.1228 

8.144 

1.008 

8.206 

1.4486 

83° 00' 

10 

251 

248 

922 

257 

7.953 

008 

8.016 

457 

50 

20 

280 

276 

918 

287 

7.770 

008 

7.834 

428 

40 

30 

.1309 

.1305 

.9914 

.1317 

7.596 

1.009 

7.661 

1.4399 

30 

40 

338 

334 

911 

346 

7.429 

009 

7.496 

370 

20 

50 

367 

363 

907 

376 

7.269 

009 

7.337 

341 

10 

8° 00' 

.1396 

.1392 

.9903 

.1405 

7.115 

1.010 

7.185 

1.4312 

00 

o 

O 

o 

10 

425 

421 

899 

435 

6.968 

010 

7.040 

283 

50 

20 

454 

449 

894 

465 

6.827 

on 

6.900 

254 

40 

30 

.1484 

.1478 

.9890 

.1495 

6.691 

1.011 

6.765 

1.4224 

30 

40 

513 

507 

886 

524 

6.561 

012 

6.636 

195 

20 

50 

542 

536 

881 

554 

6.435 

012 

6.512 

166 

10 

9° 00' 

.1571 

.1564 

.9877 

.1584 

6.314 

1.012 

6.392 

1.4137 

o 

o 

o 

00 


1 Cos 

1 Sin 

Cot 

Tan 

Csc 

Sec 

Radians 

Degrees 

















II FOUR-PLACE VALUES OF FUNCTIONS AND RADIANS 5 


Degrees 

Radians 

Sin 

Cos 

Tan 

Cot 

Sec 

Csc 



9° 00' 

10 

20 

30 

40 

50 

10° 00' 

10 

20 

30 

40 

50 

11° 00' 

10 

20 

30 

40 

50 

12 00' 

10 
20 
30 
40 
50 
13° 00' 
10 
20 
30 
40 
50 

14° 00' 

10 

20 

30 

40 

50 

15° 00' 

10 

20 

30 

40 

50 

16° 00' 

10 
20 
30 
40 
50 
17° 00' 
10 
20 
30 
40 
50 

18° 00' 

.1571 

600 

629 

.1658 

687 

716 

.1745 

774 

804 

.1833 

862 

891 

.1920 

949 

978 

.2007 

036 

065 

.2094 

123 

153 

.2182 

211 

240 

.2269 

298 

327 

.2356 

385 

414 

.2443 

473 

502 

.2531 

560 

589 

.2618 

647 

676 

.2705 

734 

763 

.2793 

822 

851 

.2880 

909 

938 

.2967 

996 

.3025 

.3054 

083 

113 

.3142 

.1564 

593 

622 

.1650 

679 

708 

.1736 

765 

794 

.1822 

851 

880 

.1908 

937 

965 

.1994 

.2022 

051 

.2079 

108 

136 

.2164 

193 

221 

.2250 

278 

306 

.2334 

363 

391 

.2419 

447 

476 

.2504 

532 

560 

.2588 

616 

644 

.2672 

700 

728 

.2756 

784 

812 

.2840 

868 

896 

.2924 

952 

979 

.3007 

035 

062 

.3090 

.9877 

872 

868 

.9863 

858 

853 

.9848 

843 

838 

.9833 

827 

822 

.9816 

811 

805 

.9799 

793 

787 

.9781 

775 

'769 

.9763 

757 

750 

.9744 

737 

730 

.9724 

717 

710 

.9703 

696 

689 

.9681 

674 

667 

.9659 

652 

644 

.9636 

628 

621 

.9613 

605 

596 

.9588 

580 

572 

.9563 

555 

546 

.9537 

528 

520 

.9511 

.1584 

614 

644 

.1673 

703 

733 

.1763 

793 

823 

.1853 

883 

914 

.1944 

974 

.2004 

.2035 

065 

095 

.2126 

156 

186 

.2217 

247 

278 

.2309 

339 

370 

.2401 

432 

462 

.2493 

524 

555 

.2586 

617 

648 

.2679 

711 

742 

.2773 

805 

836 

.2867 

899 

931 

.2962 

994 

.3026 

.3057 

089 

121 

.3153 

185 

217 

.3249 

6.314 

197 

084 

5.976 

871 

769 

5.671 

576 

485 

5.396 

309 

226 

5.145 

066 

4.989 

4.915 

843 

773 

4.705 

638 

574 

4.511 

449 
390 

4.331 

275 

219 

4.165 

113 

061 

4.011 

3.962 

914 

3.867 

821 

776 

3.732 

689 

647 

3.606 

566 

526 

3.487 

450 
412 

3.376 

340 

305 

3.271 

237 

204 

3.172 

140 

108 

3.078 

1.012 

013 

013 

1.014 

014 

015 

1.015 

016 

016 

1.017 

018 

018 

1.019 

019 

020 

1.020 

021 

022 

1.022 

023 

024 

1.024 

025 

026 

1.026 

027 

028 

1.028 

029 

030 

1.031 

031 

032 

1.033 

034 

034 

1.035 

036 

037 

1.038 

039 

039 

1.040 

041 

042 

1.043 

044 

045 

1.046 

047 

048 

1.048 

049 

050 

1.051 

6.392 

277 

166 

6.059 

5.955 

855 

5.759 

665 

575 

5.487 

403 

320 

5.241 

164 

089 

5.016 

4.945 

876 

4.810 

745 

682 

4.620 

560 

502 

4.445 

390 

336 

4.284 

232 

182 

4.134 

086 

039 

3.994 

950 

906 

3.864 

822 

782 

3.742 

703 

665 

3.628 

592 

556 

3.52] 

487 

453 

3.420 

388 

357 

3.326 

295 

265 

3.236 

1.4137 

108 

079 

1.4050 

1.4021 

992 

1.3963 

934 

904 

1.3875 

846 

817 

1.3788 

759 

730 

1.3701 

672 

643 

1.3614 

584 

555 

1.3526 

497 

468 

1.3439 

410 

381 

1.3352 

323 

294 

1.3265 

235 

206 

1.3177 

148 

119 

1.3090 

061 

032 

1.3003 

974 

945 

1.2915 

886 

857 

1.2828 

799 

770 

1.2741 

712 

683 

1.2654 

625 

595 

1.2566 

81° 00' 

50 

40 

30 

20 

10 

80° 00' 

50 

40 

30 

20 

10 

79° 00' 

50 

40 

30 

20 

10 

78° 00' 

50 

40 

30 

20 

10 

77° 00' 

50 

40 

30 

20 

10 

76° 00' 

50 

40 

30 

20 

10 

75° 00' 

50 

40 

30 

20 

10 

74° 00' 

50 

40 

30 

20 

10 

73° 00' 

50 

40 

30 

20 

10 

72° 00' 



Cos 

Sin 

Cot 

Tan 

Csc 

Sec 

Radians 

Degrees 

















6 FOUR-PLACE VALUES OF FUNCTIONS AND RADIANS II 


Degrees 

Radians 

Sin 

Cos 

Tan 

Cot 

Sec 

Csc 



18° 00' 

.3142 

.3090 

.9511 

.3249 

3.078 

1.051 

3.236 

1.2566 

72° 00' 

10 

171 

118 

502 

281 

047 

052 

207 

537 

50 

20 

200 

145 

492 

314 

018 

053 

179 

508 

40 

30 

.3229 

.3173 

.9483 

.3346 

2.989 

1.054 

3.152 

1.2479 

30 

40 

258 

201 

474 

378 

960 

056 

124 

450 

20 

50 

287 

228 

465 

411 

932 

057 

098 

421 

10 

19° 00' 

.3316 

.3256 

.9455 

.3443 

2.904 

1.058 

3.072 

1.2392 

o 

o 

o 

10 

345 

283 

446 

476 

877 

059 

046 

363 

50 

20 

374 

311 

436 

508 

850 

060 

021 

.334 

40 

30 

.3403 

.3338 

.9426 

.3541 

2.824 

1.061 

2.996 

1.2305 

30 

40 

432 

365 

417 

574 

798 

062 

971 

275 

20 

50 

462 

393 

407 

607 

773 

063 

947 

246 

10 

20° 00' 

.3491 

.3420 

.9397 

.3640 

2.747 

1.064 

2.924 

1.2217 

o 

o 

O 

o 

10 

520 

448 

387 

673 

723 

065 

901 

188 

50 

20 

549 

475 

377 

706 

699 

066 

878 

159 

40 

30 

.3578 

.3502 

.9367 

.3739 

2.675 

1.068 

2.855 

1.2130 

30 

40 

607 

529 

356 

772 

651 

069 

833 

101 

20 

50 

636 

557 

346 

805 

628 

070 

812 

072 

10 

21° 00' 

.3665 

.3584 

.9336 

.3839 

2.605 

1.071 

2.790 

1.2043 

69° 00' 

10 

694 

611 

325 

872 

583 

072 

769 

1.2014 

50 

20 

723 

638 

315 

906 

560 

074 

749 

985 

40 

30 

.3752 

.3665 

.9304 

.3939 

2.539 

1.075 

2.729 

1.1956 

30 

40 

782 

692 

293 

973 

517 

076 

709 

926 

20 

50 

811 

719 

283 

.4006 

496 

077 

689 

897 

10 

22° 00' 

.3840 

.3746 

.9272 

.4040 

2.475 

1.079 

2.669 

1.1868 

68° 00' 

10 

869 

773 

261 

074 

455 

080 

650 

839 

50 

20 

898 

800 

250 

108 

434 

081 

632 

810 

40 

30 

.3927 

.3827 

.9239 

.4142 

2.414 

1.082 

2.613 

1.1781 

30 

40 

956 

854 

228 

176 

394 

084 

595 

752 

20 

50 

985 

881 

216 

210 

375 

085 

577 

723 

10 

23° 00' 

.4014 

.3907 

.9205 

.4245 

2.356 

1.086 

2.559 

1.1694 

67° 00' 

10 

043 

934 

194 

279 

337 

088 

542 

665 

50 

20 

072 

961 

182 

314 

318 

089 

525 

636 

40 

30 

.4102 

.3987 

.9171 

.4348 

2.300 

1.090 

2.508 

1.1606 

30 

40 

131 

.4014 

159 

383 

282 

092 

491 

577 

20 

50 

160 

041 

147 

417 

264 

093 

475 

548 

10 

o 

O 

o 

.4189 

.4067 

.9135 

.4452 

2.246 

1.095 

2.459 

1.1519 

66° 00' 

10 

218 

094 

124 

487 

229 

096 

443 

490 

50 

20 

247 

120 

112 

522 

211 

097 

427 

461 

40 

30 

.4276 

.4147 

.9100 

.4557 

2.194 

1.099 

2.411 

1.1432 

30 

40 

305 

173 

088 

592 

177 

100 

396 

403 

20 

50 

334 

200 

075 

628 

161 

102 

381 

374 

10 

25° 00' 

.4363 

.4226 

.9063 

.4663 

2.145 

1.103 

2.366 

1.1345 

65° 00' 

10 

392 

253 

051 

699 

128 

105 

352 

316 

50 

20 

422 

279 

038 

734 

112 

106 

337 

286 

40 

30 

.4451 

.4305 

.9026 

.4770 

2.097 

1.108 

2.323 

1.1257 

30 

40 

480 

331 

013 

806 

081 

109 

309 

228 

20 

50 

509 

358 

001 

841 

066 

111 

295 

199 

10 

26° 00' 

.4538 

.4384 

.8988 

.4877 

2.050 

1.113 

2.281 

1.1170 

64° 00' 

10 

567 

410 

975 

913 

035 

114 

268 

141 

50 

20 

596 

436 

962 

950 

020 

116 

254 

112 

40 

30 

.4625 

.4462 

.8949 

.4986 

2.006 

1.117 

2.241 

1.1083 

30 

40 

654 

488 

936 

.5022 

1.991 

119 

228 

054 

20 

50 

683 

514 

923 

059 

977 

121 

215 

1.1025 

10 

27° 00' 

.4712 

.4540 

.8910 

.5095 

1.963 

1.122 

2.203 

1.0996 

63° 00' 



Cos 

Sin 

Cot 

Tan 

Csc 

Sec 

Radians 

Degrees 




















II FOUR-PLACE values OF FUNCTIONS AND RADIANS 7 


Degrees 

Radians 

Sin 

Cos 

Tan 

Cot 

Sec 

Csc 



27 ° 00' 

.4712 

.4540 

.8910 

.5095 

1.963 

1.122 

2.203 

1.0996 

63° 00' 

10 

741 

566 

897 

132 

949 

124 

190 

966 

50 

20 

771 

592 

884 

169 

935 

126 

178 

937 

40 

30 

.4800 

.4617 

.8870 

.5206 

1.921 

1.127 

2.166 

1.0908 

30 

40 

829 

643 

857 

243 

907 

129 

154 

879 

20 

50 

858 

669 

843 

280 

894 

131 

142 

850 

10 

28° 00' 

.4887 

.4695 

.8829 

.5317 

1.881 

1.133 

2.130 

1.0821 

62° 00' 

10 

916 

720 

816 

354 

868 

134 

118 

792 

50 

20 

945 

746 

802 

392 

855 

136 

107 

763 

40 

30 

.4974 

.4772 

.8788 

.,5430 

1.842 

1.138 

2.096 

1.0734 

30 

40 

.5003 

797 

774 

467 

829 

140 

085 

705 

20 

50 

032 

823 

760 

505 

816 

142 

074 

676 

10 

29° 00' 

.5061 

.4848 

.8746 

.5543 

1.804 

1.143 

2.063 

1.0647 

61° 00' 

10 

091 

874 

732 

581 

792 

145 

052 

617 

50 

20 

120 

899 

718 

619 

780 

147 

041 

588 

40 

30 

.5149 

.4924 

.8704 

.5658 

1.767 

1.149 

2.031 

1.0559 

30 

40 

178 

950 

689 

696 

756 

151 

020 

530 

20 

50 

207 

975 

675 

735 

744 

153 

010 

501 

10 

30° 00' 

.5236 

.5000 

.8660 

.5774 

1.732 

1.155 

2.000 

1.0472 

60° 00' 

10 

265 

025 

646 

812 

720 

157 

1.990 

443 

50 

20 

294 

050 

631 

851 

709 

159 

980 

414 

40 

30 

.5323 

.5075 

.8616 

.5890 

1.698 

1.161 

1.970 

1.0385 

30 

40 

352 

100 

601 

930 

686 

163 

961 

356 

20 

50 

.381 

125 

587 

969 

.675 

165 

951 

327 

10 

31° 00' 

.5411 

.5150 

.8572 

.6009 

1.664 

1.167 

1.942 

1.0297 

59° 00' 

10 

440 

175 

557 

048 

653 

169 

932 

268 

50 

20 

469 

200 

542 

088 

643 

171 

923 

239 

40 

30 

.5498 

.5225 

.8526 

.6128 

1.632 

1.173 

1.914 

1.0210 

30 

40 

527 

250 

511 

168 

621 

175 

905 

181 

20 

50 

556 

275 

496 

208 

611 

177 

896 

152 

10 

32° 00' 

.5585 

.5299 

.8480 

.6249 

1.600 

1.179 

1.887 

1.0123 

58° 00' 

10 

614 

324 

465 

289 

590 

181 

878 

094 

50 

20 

643 

348 

450 

330 

580 

184 

870 

065 

40 

30 

.5672 

.5373 

.8434 

.6371 

1.570 

1.186 

1.861 

1.0036 

30 

40 

701 

398 

418 

412 

560 

188 

853 

1.0007 

20 

50 

730 

422 

403 

453 

550 

190 

844 

977 

10 

33° 00' 

.5760 

.5446 

.8387 

.6494 

1.540 

1.192 

1.836 

.9948 

57° 00' 

10 

789 

471 

371 

536 

530 

195 

828 

919 

50 

20 

818 

495 

355 

577 

520 

197 

820 

890 

40 

30 

.5847 

.5519 

.8339 

.6619 

1.511 

1.199 

1.812 

.9861 

30 

40 

876 

544 

323 

661 

501 

202 

804 

832 

20 

50 

905 

568 

307 

703 

1.492 

204 

796 

803 

10 

34° 00' 

.5934 

.5592 

.8290 

.6745 

1.483 

1.206 

1.788 

.9774 

56° 00' 

10 

963 

616 

274 

787 

473 

209 

781 

745 

50 

20 

992 

640 

258 

830 

464 

211 

773 

716 

40 

30 

.6021 

.5664 

.8241 

.6873 

1.455 

1.213 

1.766 

.9687 

30 

40 

050 

688 

225 

916 

446 

216 

758 

657 

20 

50 

080 

712 

208 

959 

437 

218 

751 

628 

10 

35° 00' 

.6109 

.5736 

.8192 

.7002 

1.428 

1.221 

1.743 

.9599 

55° 00' 

10 

138 

760 

175 

046 

419 

223 

736 

570 

50 

20 

167 

783 

158 

089 

411 

226 

729 

541 

40 

30 

.6196 

.5807 

.8141 

.7133 

1.402 

1.228 

1.722 

.9512 

30 

40 

225 

831 

124 

177 

.393 

231 

715 

483 

20 

50 

254 

854 

107 

221 

385 

233 

708 

454 

10 

36° 00' 

.6283 

.5878 

.8090 

.7265 

1.376 

1.236 

1.701 

.9425 

54° 00' 


1 

Cos 

Sin 

Cot 

Tan 

Csc 

Sec 

Radians 

Degrees 




















8 FOUR-PLACE VALUES OF FUNCTIONS AND RADIANS II 


Degrees 

Radians 

Sin 

Cos 

Tan 

Cot 

Sec 

Csc 



36° 00' 

.6283 

.5878 

.8090 

.7265 

1.376 

1.236 

1.701 

.9425 

54° 00' 

10 

312 

901 

073 

310 

368 

239 

695 

396 

50 

20 

341 

925 

056 

355 

360 

241 

688 

367 

40 

30 

.6370 

.5948 

.8039 

.7400 

1.351 

1.244 

1.681 

.9338 

30 

40 

400 

972 

021 

445 

343 

247 

675 

308 

20 

50 

429 

995 

004 

490 

335 

249 

668 

279 

10 

37° 00' 

.6458 

.6018 

.7986 

.7536 

1.327 

1.252 

1.662 

.9250 

53° 00' 

10 

487 

041 

969 

581 

319 

255 

655 

221 

50 

20 

516 

065 

951 

627 

311 

258 

649 

192 

40 

30 

.6545 

.6088 

.7934 

.7673 

1.303 

1.260 

1.643 

.9163 

30 

40 

574 

111 

916 

720 

295 

263 

636 

134 

20 

50 

603 

134 

898 

766 

288 

266 

630 

105 

10 

38° 00' 

.6632 

.6157 

.7880 

.7813 

1.280 

1.269 

1.624 

.9076 

52° 00' 

10 

661 

180 

862 

860 

272 

272 

618 

047 

50 

20 

690 

202 

844 

907 

265 

275 

612 

.9018 

40 

30 

.6720 

.6225 

.7826 

.7954 

1.257 

1.278 

1.606 

.8988 

30 

40 

749 

248 

808 

.8002 

250 

281 

601 

959 

20 

50 

778 

271 

790 

050 

242 

284 

595 

930 

10 

39° 00' 

.6807 

.6293 

.7771 

.8098 

1.235 

1.287 

1.589 

.8901 

cn 

o 

O 

O 

10 

836 

316 

753 

146 

228 

290 

583 

872 

50 

20 

865 

338 

735 

195 

220 

293 

578 

843 

40 

30 

.6894 

.6361 

.7716 

.8243 

1.213 

1.296 

1.572 

.8814 

30 

40 

923 

383 

698 

292 

206 

299 

567 

785 

20 

50 

952 

406 

679 

342 

199 

302 

561 

756 

10 

40° 00' 

.6981 

.6428 

.7660 

.8391 

1.192 

1.305 

1.556 

.8727 

50° 00' 

10 

.7010 

450 

642 

441 

185 

309 

550 

698 

50 

20 

039 

472 

623 

491 

178 

312 

545 

668 

40 

30 

.7069 

.6494 

.7604 

.8541 

1.171 

1.315 

1.540 

.8639 

30 

40 

098 

517 

585 

591 

164 

318 

535 

610 

20 

50 

127 

539 

566 

642 

157 

322 

529 

581 

10 

41° 00' 

.7156 

.6561 

.7547 

.8693 

1.150 

1.325 

1.524 

.8552 

49° 00' 

10 

185 

583 

528 

744 

144 

328 

519 

523 

50 

20 

214 

604 

509 

796 

137 

332 

514 

494 

40 

30 

.7243 

.6626 

.7490 

.8847 

1.130 

1.335 

1.509 

.8465 

30 

40 

272 

648 

470 

899 

124 

339 

504 

436 

20 

50 

301 

670 

451 

952 

117 

342 

499 

407 

10 

42° 00' 

.7330 

.6691 

.7431 

.9004 

1.111 

1.346 

1.494 

.8378 

48° 00' 

10 

359 

713 

412 

057 

104 

349 

490 

348 

50 

20 

389 

734 

392 

110 

098 

353 

485 

319 

40 

30 

.7418 

.6756 

.7373 

.9163 

1.091 

1.356 

1.480 

.8290 

30 

40 

447 

777 

353 

217 

085 

360 

476 

261 

20 

50 

476 

799 

333 

271 

079 

364 

471 

232 

10 

43° 00' 

.7505 

.6820 

.7314 

.9325 

1.072 

1.367 

1.466 

.8203 

47° 00' 

10 

534 

841 

294 

380 

066 

371 

462 

174 

50 

20 

563 

862 

274 

435 

060 

375 

457 

145 

40 

30 

.7592 

.6884 

.7254 

.9490 

1.054 

1.379 

1.453 

.8116 

30 

40 

621 

905 

234 

545 

048 

382 

448 

087 

20 

50 

650 

926 

214 

601 

042 

386 

444 

058 

10 

44° 00' 

.7679 

.6947 

.7193 

.9657 

1.036 

1.390 

1.440 

.8029 

46° 00' 

10 

709 

967 

173 

713 

030 

394 

435 

999 

50 

20 

738 

988 

153 

770 

024 

398 

431 

970 

40 

30 

.7767 

.7009 

.7133 

.9827 

1.018 

1.402 

1.427 

.7941 

30 

40 

796 

030 

112 

884 

012 

406 

423 

912 

20 

50 

825 

050 

092 

942 

006 

410 

418 

883 

10 

45° 00' 

.7854 

.7071 

.7071 

1.000 

1.000 

1.414 

1.414 

.7854 

45° 00' 



Cos 

Sin 

Cot 

Tan 

Csc 

Sec 

Radians 

Degrees 

































10 


FOUR-PLACE LOGARITHMS OF NUMBERS 


III 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Proportional Parts 

1 

2 

3 

; 4 

5 

6 

7 8 9 

1.0 

0000 

043 

086 

128 

170 

212 

253 

294 

334 

374 

4 

8 12 

: 17 21 25 


1 

414 

453 

492 

531 

569 

607 

645 

682 

719 

755 

4 

8 11 

15 19 23 


2 

792 

828 

864 

899 

934 

969 

*004 

*038 

*072 

*106 

3 

7 10 

'1 14 17 21 

O ea Cl 

3 

1139 

173 

206 

239 

271 

303 

335 

367 

399 

430 

3 

6 10 

I 13 16 19 

« g ^ 

4 

461 

492 

523 

553 

584 

614 

644 

673 

703 

732 

3 

6 

9 

1 12 15 18 


1.5 

761 

790 

818 

847 

875 

903 

931 

959 

987 

*014 

3 

6 

8 

11 14 17 


6 

2041 

068 

095 

122 

148 

175 

201 

227 

253 

279 

3 

5 

8 

11 13 16 

.£h 0) <D 

7 

304 

330 

355 

380 

405 

430 

455 

480 

504 

529 

2 

5 

7 

10 12 15 


8 

553 

577 

601 

625 

648 

672 

695 

718 

742 

765 

2 

5 

7 

9 12 14 

^ » C 

9 

788 

810 

833 

856 

878 

900 

923 

945 

967 

989 

2 

4 

7 

9 11 13 

Pi o3 

2.0 

3010 

032 

054 

075 

096 

118 

139 

160 

181 

201 

2 

4 

6 

8 11 13 

15 17 19 

1 

222 

243 

263 

284 

304 

324 

345 

365 

385 

404 

2 

4 

6 

8 10 12 

14 16 18 

2 

424 

444 

464 

483 

502 

522 

541 

560 

! 579 

598 

2 

4 

6 

8 10 12 

14 16 17 

3 

617 

636 

655 

674 

692 

711 

729 

747 

766 

784 

2 

4 

6 

7 

9 11 

13 15 17 

4 

802 

820 

838 

856 

874 

892 

909 

927 

945 

962 

2 

4 

5 

7 

9 11 

12 14 16 

2.5 

979 

997 

*014 

*031 

*048 

*065 

*082 

*099 

*116 

*133 

2 

4 

5 

7 

9 10 

12 14 16 

6 

4150 

166 

183 

200 

216 

232 

249 

265 

281 

298 

2 

3 

5 

7 

8 10 

11 13 15 

7 

314 

330 

346 

362 

378 

393 

409 

425 

440 

456 

2 

3 

5 

6 

8 

9 

11 12 14 

8 

472 

487 

502 

518 

533 

548 

564 

579 

594 

609 

2 

3 

5 

6 

8 

9 

11 12 14 

9 

624 

639 

654 

669 

683 

698 

713 

728 

742 

757 

1 

3 

4 

6 

7 

9 

10 12 13 

3.0 

771 

786 

800 

814 

829 

843 

857 

871 

886 

900 

1 

3 

4 

6 

7 

9 

10 11 13 

1 

914 

928 

942 

955 

969 

983 

997 

*011 

*024 

*038 

1 

3 

4 

5 

7 

8 

10 11 12 

2 

5051 

065 

079 

092 

105 

119 

132 

145 

159 

172 

1 

3 

4 

5 

7 

8 

9 11 12 

3 

185 

198 

211 

224 

237 

250 

263 

276 

289 

302 

1 

3 

4 

5 

7 

8 

9 11 12 

4 

315 

328 

340 

353 

366 

378 

391 

403 

416 

428 

1 

2 

4 

5 

6 

8 

9 10 11 

3.5 

441 

453 

465 

478 

490 

502 

514 

527 

539 

551 

1 

2 

4 

5 

6 

7 

9 10 11 

6 

563 

575 

587 

599 

611 

623 

635 

647 

658 

670 

1 

2 

4 

5 

6 

7 

8 10 11 

7 

682 

694 

705 

717 

729 

740 

752 

763 

775 

786 

1 

2 

4 

5 

6 

7 

8 9 11 

8 

798 

809 

821 

832 

843 

855 

866 

877 

888 

899 

1 

2 

3i 

5 

6 

7 

8 9 10 

9 

911 

922 

933 

944 

955 

966 

977 

988 

999 

*010 

1 

2 

3 

4 

5 

7 

8 9 10 

4.0 

6021 

031 

042 

053 

064 

075 

085 

096 

107 

117 

1 

2 

3 

4 

5 

6 

8 9 10 

1 

128 

138 

149 

160 

170 

180 

191 

201 

212 

222 

1 

2 

3 

4 

5 

6 

7 8 9 

2 

232 

243 

253 

263 

274 

284 

294 

304 

314 

325 

1 

2 

3 

4 

5 

6 

7 8 9 

3 

335 

345 

355 

365 

375 

385 

395 

405 

415 

425 

1 

2 

3 

4 

5 

6 

7 8 9 

4 

435 

444 

454 

464 

474 

484 

493 

503 

513 

522 

1 

2 

3 

4 

5 

6 

7 8 9 

4.5 

532 

542 

551 

561 

571 

580 

590 

599 

609 

618 

1 

2 

3 

4 

5 

6 

7 8 9 

6 

628 

637 

646 

656 

665 

675 

684 

693 

702 

712 

1 

2 

3 

4 

5 

6 

7 7 8 

7 

721 

730 

739 

749 

758 

767 

776 

785 

794 

803 

1 

2 

3 

4 

5 

6 

7 7 8 

8 

812 

821 

830 

839 

848 

857 

866 

875 

884 

893 

1 

2 

3 

4 

5 

6 

7 7 8 

9 

902 

911 

920 

928 

937 

946 

955 

964 

972 

981 

1 

2 

3 

4 

4 

5 

6 7 8 

5.0 

990 

998 

*007 

*016 

*024 

*033 

*042 

*050 

*059 

*067 

1 

2 

3 

3 

4 

5 

6 7 8 

1 

7076 

084 

093 

101 

110 

118 

126 

135 

143 

152 

1 

2 

3 

3 

4 

5 

6 7 8 

2 

160 

168 

177 

185 

193 

202 

210 

218 

226 

235 

1 

2 

3 

3 

4 

5 

6 7 7 

3 

243 

251 

259 

267 

275 

284 

292 

300 

308 

316 

1 

2 

2 

3 

4 

5 

6 6 7 

4 

324 

332 

340 

348 

356 

364 

372 

380 

388 

396 

1 

2 

2 

3 

4 

5 

6 6 7 

N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

2 

3 

4 

5 

6 

7 8 9 
























































































































































Ill 


FOUR-PLACE LOGARITHMS OF NUMBERS 


11 


N 

0 

1 

2 

3 

4 

5 

e 

7 

8 

I 

9 

Proportional Parts 

1 

2 

3 

4 

5 

6 

7 8 

9 

5.5 

7404 

412 

419 

427 

435 

443 

451 

459 

466 

474 

1 

2 

2 

3 

4 

5 

5 

6 

7 

6 

482 

490 

497 

505 

513 

520 

528 

536 

543 

551 

1 

2 

2 

3 

4 

5 

5 

6 

7 

7 

559 

566 

574 

582 

589 

597 

604 

612 

619 

627 

1 

1 

2 

3 

4 

5 

5 

6 

7 

8 

634 

642 

649 

657 

664 

672 

679 

686 

694 

701 

1 

1 

2 

3 

4 

4 

5 

6 

7 

9 

709 

716 

723 

731 

738 

745 

752 

760 

767 

774 

1 

1 

2 

3 

4 

4 

5 

6 

7 

6.0 

782 

789 

796 

803 

810 

818 

825 

832 

839 

846 

1 

1 

2 

3 

4 

4 

5 

6 

6 

1 

853 

860 

868 

875 

882 

889 

896 

903 

910 

917 

1 

1 

2 

3 

3 

4 

5 

6 

6 

2 

924 

931 

938 

945 

952 

959 

966 

973 

980 

987 

1 

1 

2 

3 

3 

4 

5 

5 

6 

3 

993 

*000 

*007 

*014 

*021 

*028 

*035 

*041 

*048 

*055 

1 

1 

2 

3 

3 

4 

5 

6 

6 

4 

8062 

069 

075 

082 

089 

096 

102 

109 

116 

122 

1 

1 

2 

3 

3 

4 

5 

5 

6 

6.5 

129 

136 

142 

149 

156 

162 

169 

176 

182 

189 

1 

1 

2 

3 

3 

4 

5 

5 

6 

6 

195 

202 

209 

215 

222 

228 

235 

241 

248 

254 

1 

1 

2 

3 

3 

4 

5 

5 

6 

7 

261 

267 

274 

280 

287 

293 

299 

306 

312 

319 

1 

1 

2 

3 

3 

4 

5 

5 

6 

8 

325 

331 

338 

344 

351 

357 

363 

370 

376 

i 382 

1 

1 

2 

! 3 

3 

4 

i 4 

5 

6 

9 

388 

395 

401 

407 

414 

420 

426 

432 

439 

445 

1 

1 

2 

3 

3 

4 

i 4 

5 

6 

7.0 

451 

457 

463 

470 

476 

482 

488 

494 

500 

506 

1 

1 

2 

3 

3 

4 

4 

5 

6 

1 

513 

519 

525 

531 

537 

543 

549 

555 

561 

567 

1 

1 

2 

3 

3 

4 

4 

5 

6 

2 

573 

579 

585 

591 

597 

603 

609 

615 

621 

627 

1 

1 

2 

3 

3 

4 

4 

5 

6 

3 

633 

639 

645 

651 

657 

663 

669 

675 

681 

686 

1 

1 

2 

2 

3 

4 

4 

5 

5 

4 

692 

698 

704 

710 

716 

722 

727 

733 

739 

745 

1 

1 

2 

2 

3 

4 

4 

5 

5 

7.5 

751 

756 

762 

768 

774 

779 

785 

791 

797 

802 

1 

1 

2 

2 

3 

3 

4 

5 

5 

6 

808 

814 

820 

825 

831 

837 

842 

848 

854 

859 

1 

1 

2 

2 

3 

3 

4 

4 

5 

7 

865 

871 

876 

882 

887 

893 

899 

904 

910 

915 

1 

1 

2 

2 

3 

3 

4 

4 

5 

8 

921 

927 

932 

938 

943 

949 

954 

960 

965 

971 

1 

1 

2 

2 

3 

3 

4 

4 

5 

9 

976 

982 

987 

993 

998 

*004 

*009 

*015 

*020 

*025 

1 

1 

2 

2 

3 

3 

4 

4 

5 

8.0 

9031 

036 

042 

047 

053 

058 

063 

069 

074' 

079 

1 

1 

2 

2 

3 

3 

4 

4 

5 

1 

085 

090 

096 

101 

106 

112 

117 

122 

128 

133 

1 

1 

2 

2 

3 

3 

4 

4 

5 

2 

138 

143 

149 

154 

159 

165 

170 

175 

180 

186 

1 

1 

2 

2 

3 

3 

4 

4 

5 

3 

191 

196 

201 

206 

212 

217 

222 

227 

232 

238 

1 

1 

2 

2 

3 

3 

4 

4 

5 

4 

243 

248 

253 

258 

263 

269 

274 

279 

284 

289 

1 

1 

2 

2 

3 

3 

4 

4 

5 

8.5 

294 

299 

304 

309 

315 

320 

325 

330 

335 

340 

1 

1 

2 

2 

3 

3 

4 

4 

5 

6 

345 

350 

355 

360 

365 

370 

375 

380 

385 

390 

1 

1 

2 

2 

3 

3 

4 

4 

5 

7 

395 

400 

405 

410 

415 

420 

425 

430 

435 

440 

1 

1 

2 

2 

3 

3 

4 

4 

5 

8 

445 

450 

455 

460 

465 

469 

474 

479 

484 

489 

0 

1 

1 

2 

2 

3 

3 

4 

4 

9 

494 

499 

504 

509 

513 

518 

523 

528 

533 

538 

0 

1 

1 

2 

2 

3 

3 

4 

4 

9.0 

542 

547 

552 

557 

562 

566 

571 

576 

581 

586 

0 

1 

1 

2 

2 

3 

3 

4 

4 

1 

590 

595 

600 

605 

609 

614 

619 

624 

628 

633 

0 

1 

1 1 

2 

2 

3 

3 

4 

4 

2 

638 

643 

647 

652 

657 

661 

666 

671 

675 

680 

0 

1 

1 

2 

2 

3 

3 

4 

4 

3 

685 

689 

694 

699 

703 

708 

713 

717 

722 

727 

0 

1 

1 

2 

2 

3 

3 

4 

4 

4 

731 

736 

741 

745 

750 

754 

759 

763 

768 

773 

0 

1 

1 

2 

2 

3 

3 

4 

4 

9.5 

777 

782 

786 

791 

795 

800 

805 

809 

814 

818 

0 

1 

1 

2 

2 

3 

3 

4 

4 

6 

823 

827 

832 

836 

841 

845 

850 

854 

859 

863 

0 

1 

1 

2 

2 

3 

3 

4 

4 

7 

868 

872 

877 

881 

886 

890 

894 

899 

903 

908 

0 

1 

1 

2 

2 

3 

3 

4 

4 

8 

912 

917 

921 

926 

930 

934 

939 

943 

948 

952 

0 

1 

1 

2 

2 

3 

3 

3 

4 

9 

956 

961 

965 

969 

974 

978 

983 

987 

991 

996 

0 

1 

1 

2 

2 

3 

3 

3 

4 

N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1 

2 

3 

4 

5 

6 

7 

8 

9 







































































































































TABLE IV 


FOUR-PLACE LOGARITHMS 
OF TRIGONOMETRIC FUNCTIONS 


Note 1. — For simplicity in printing, all characteristics have been increased by 10. 
Hence 10 must be subtracted from each tabulated value of a logarithm. 

Note 2. — To avoid interpolating for angles between 0° and 3° or 87° and 90° 
use Tables V a or V 6. 


Angle 

L Sin 

dl' 

L Tan 

c dl' 

L Cot 

L Cos 

dl' 


0° 0' 

10' 

20' 

30' 

40' 

50' 

1° 0' 

10' 

20' 

30' 

40' 

50' 

2° 0' 

10' 

20' 

30' 

40' 

50' 

3° 0' 

10' 

20' 

30' 

40' 

50' 

4° 0' 

10' 

20' 

30' 

40' 

50' 

5° 0' 

7.4637 

.7648 

.9408 

8.0658 

.1627 

301.1 

176.0 

125.0 

96.9 

79.2 

66.9 

58.0 

51.1 

45.8 

41.3 

37.8 

34.8 

32.1 
30.0 
28.0 

26.3 

24.8 

23.5 

22.2 
21.2 
20.2 

19.2 

18.5 

17.7 

17.0 

16.3 

15.8 
15.2 
14.7 

7.4637 

.7648 

.9409 

8.0658 

.1627 

301.1 

176.1 
124.9 

96.9 

79.2 

67.0 

58.0 

51.2 

45.7 

41.5 

37.8 

34.8 

32.2 
30.0 
28.1 

26.3 

24.9 

23.5 

22.3 

21.3 
20.2 

19.4 

18.5 

17.8 

17.1 

16.5 

15.8 
15.4 

14.8 

12.5363 

.2352 

.0591 

11.9342 

.8373 

10.0000 

.0 

.0 

.0 

.0 

.0 

.1 

.0 

.0 

.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.0 

.1 

.1 

.0 

.1 

.1 

.1 

.1 

.0 

.1 

.1 

.1 

.1 

.2- 

90° 0' 

50' 

40' 

30' 

20' 

10' 

89° 0' 

50' 

40' 

30' 

20' 

10' 

88° 0' 

50' 

40' 

30' 

20' 

10' 

87° 0' 

50' 

40' 

30' 

20' 

10 

86° 0' 

50' 

40' 

30' 

20' 

10' 

85° 0' 

.0000 

.0000 

.0000 

.0000 

.0000 

8.2419 

8.2419 

11.7581 

9.9999 

.3088 

.3668 

.4179 

.4637 

.5050 

.3089 

.3669 

.4181 

.4638 

.5053 

.6911 

.6331 

.5819 

.5362 

.4947 

.9999 

.9999 

.9999 

.9998 

.9998 

8.5428 

8.5431 

11.4569 

9.9997 

.5776 

.6097 

.6397 

.6677 

.6940 

.5779 

.6101 

.6401 

.6682 

.6945 

.4221 

.3899 

.3599 

.3318 

.3055 

.9997 

.9996 

.9996 

.9995 

.9995 

8.7188 

8.7194 

11.2806 

9.9994 

.7423 

.7645 

.7857 

.8059 

.8251 

.742^ 

.76.52 

.7865 

.8067 

.8261 

.2571 

.2348 

.2135 

.1933 

.1739 

.9993 

.9993 

.9992 

.9991 

.9990 

8.8436 

8.8446 

11.1554 

9.9989 

.8613 

.8783 

.8946 

.9104 

.9256 

.8624 

.8795 

.8960 

.9118 

.9272 

.1376 

.1205 

.1040 

.0882 

.0728 

.9989 

.9988 

.9987 

.9986 

.9985 

8.9403 

8.9420 

11.0580 

9.9983 


L Cos 

dl' 

L Cot 

c d 1' 

L Tan 

L Sin 

d 1' 

Angle 


12 



































































IV 


FOUR-PLACE LOGARITHMS OF FUNCTIONS 


13 


Angle L Sin 


5° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

6 ° 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

70 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

8 ° 0 ' 

10 ' 

20' 

30' 

40' 

50' 

9° 0' 

10' 

20 ' 

30' 

40' 

50' 

10 ° 0 ' 

10' 

20 ' 

30' 

40' 

50' 

11 ° 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

12 ° 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

13° 0' 


8.9403 


.9545 

.9682 

.9816 

.9945 

9.0070 

9.0192 

.0311 

.0426 

.0539 

.0648 

.0755 

9.0859 

.0961 

.1060 

.1157 

.1252 

.1345 

9.1436 

.1525 

.1612 

.1697 

.1781 

.1863 

9.1943 

.2022 

.2100 

.2176 

.2251 

.2324 

9.2397 

.2468 

.2538 

.2606 

.2674 

.2740 

9.2806 

.2870 

.2934 

.2997 

.3058 

.3119 

9.3179 

.3238 

.3296 

.3353 

.3410 

.3466 


9.3521 


L Cos 


d 1' 


14.2 

13.7 

13.4 

12.9 

12.5 

12.2 

11.9 

11.5 

11.3 

10.9 

10.7 

10.4 

10.2 

9.9 

9.7 

9.5 

9.3 

9.1 

8.9 

8.7 

8.5 

8.4 

8.2 
8.0 

7.9 

7.8 

7.6 

7.5 
7.3 

7.3 

7.1 

7.0 

6.8 
6.8 

6.6 
6.6 

6.4 

6.4 
6.3 

6.1 
6.1 
6.0 

5.9 

5.8 

5.7 

5.7 

5.6 

5.5 


d 1' 


L Tan 

8.9420 

.9563 

.9701 

.9836 

.9966 

9.0093 

9.0216 

.0336 

.0453 

.0567 

.0678 

.0786 

9.0891 

.0995 

.1096 

.1194 

.1291 

.1385 

9.1478 

.1569 

.1658 

.1745 

.1831 

.1915 

9.1997 

.2078 

.2158 

.2236 

.2313 

.2389 

9.2463 

.2536 

.2609 

.2680 

.2750 

.2819 

9.2887 

.2953 

.3020 

.3085 

.3149 

.3212 

9.3275 

.3336 

.3397 

.3458 

.3517 

.3576 

9.3634 

L Cot 


cd 1' 


14.3 

13.8 

13.5 

13.0 

12.7 

12.3 

12.0 

11.7 

11.4 
11.1 

10.8 

10.5 

10.4 

10.1 

9.8 

9.7 
9.4 

9.3 

9.1 

8.9 

8.7 

8.6 

8.4 

8.2 

8.1 

8.0 

7.8 

7.7 

7.6 

7.4 

7.3 

7.3 

7.1 
7.0 

6.9 

6.8 

6.6 

6.7 

6.5 

6.4 
6.3 
6.3 

6.1 

6.1 

6.1 

5.9 
5.9 

5.8 


cd 1' 


L Cot 

L Cos 

11.0580 

9.9983 

.0437 

.9982 

.0299 

.9981 

.0164 

.9980 

.0034 

.9979 

10.9907 

.9977 

10.9784 

9.9976 

.9664 

.9975 

.9547 

.9973 

.9433 

.9972 

.9322 

.9971 

.9214 

.9969 

10.9109 

9.9968 

.9005 

.9966 

.8904 

.9964 

.8806 

.9963 

.8709 

.9961 

.8615 

.9959 

10.8522 

9.9958 

.8431 

.9956 

.8342 

.9954 

.8255 

.9952 

.8169 

.9950 

.8085 

.9948 

10.8003 

9.9946 

.7922 

.9944 

.7842 

.9942 

.7764 

.9940 

.7687 

.9938 

.7611 

.9936 

10.7537 

9.9934 

.7464 

.9931 

.7391 

.9929 

.7320 

.9927 

.7250 

.9924 

.7181 

.9922 

10.7113 

9.9919 

.7047 

.9917 

.6980 

.9914 

.6915 

.9912 

.6851 

.9909 

.6788 

.9907 

10.6725 

9.9904 

.6664 

.9901 

.6603 

.9899 

.6542 

.9896 

.6483 

.9893 

.6424 

.9890 

10.6366 

9.9887 

L Tan 

L Sin 


d 1' 


d r 


85° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

84° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

83° 0' 

.50' 

40' 

30' 

20 ' 

10 ' 

82° 0 ' 

50' 

40' 

30' 

20 ' 

10 ' 

81° 0 ' 

50' 

40' 

30' 

20 ' 

10 ' 

80° 0 ' 

50' 

40' 

30' 

20 ' 

10 ' 

79° 0' 

50' 
40' 
30' 
20 ' 
10 ' 
78° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

77° 0' 


Angle 







































































14 


FOUR-PLACE LOGARITHMS OF FUNCTIONS 


IV 


Angle 


13° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

14° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

15° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

16° 0' 

10 ' 

20 ' 

30' 

40 

50' 

17° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

18° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

19° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

20 ° 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

21 ° 0 ' 


L Sin 

9.3521 

.3575 

.3629 

.3682 

.3734 

.3786 

9.3837 

.3887 

.3937 

.3986 

.4035 

.4083 

9.4130 

.4177 

.4223 

.4269 

.4314 

.4359 

9.4403 

.4447 

.4491 

.45.33 

.4576 

.4618 

9.4659 

.4700 

.4741 

.4781 

.4821 

.4861 

9.4900 

.4939 

.4977 

.5015 

.5052 

.5090 

9.5126 

.5163 

.5199 

.5235 

.5270 

.5306 

9.5341 

.5375 

.5409 

.5443 

.5477 

.5510 

9.5543 

L Cos 


d V 


5.4 

5.4 

5.3 
5.2 
5.2 

5.1 

5.0 

5.0 

4.9 

4.9 

4.8 
4.7 

4.7 

4.6 

4.6 

4.5 

4.5 

4.4 

4.4 

4.4 

4.2 

4.3 

4.2 

4.1 

4.1 

4.1 

4.0 

4.0 

4.0 

3.9 

3.9 

3.8 
3.8 

3.7 

3.8 

3.6 

3.7 

3.6 

3.6 

3.5 

3.6 
3.5 

3.4 

3.4 

3.4 

3.4 

3.3 
3.3 


d 1' 


L Tan 

c d 1' 

j L Cot 

L Cos 

dl' 


9.3634 

5.7 

i 10.6366 

9.9887 

.3 

77° 0' 

.3691 

1 .6309 

.9884 

50' 

.3748 

5.7 

1 .6252 

.9881 

.3 

40' 

.3804 

5.6 

1 .6196 

.9878 

.3 

30' 

.3859 

5.5 

.6141 

.9875 

.3 

20' 

.3914 

5.5 

5.4 

5.3 

.6086 

.9872 

.3 

.3 

.3 

10' 

9.3968 

1 10.6032 

9.9869 

76° 0' 

.4021 

i .5979 

.9866 

50' 

.4074 

5..3 

' .5926 

.9863 

.3 

40' 

.4127 

5.3 

.5873 

.9859 

.4 

30' 

.4178 

5.1 

.5822 

.9856 

..3 

20' 

.4230 

5.2 

5.1 

5.0 

.5770 

.9853 

.3 

A 

10' 

9.4281 

10.5719 

9.9849 

.‘x 

.3 

75° 0' 

.4331 

.5669 

.9846 

50' 

.4381 

5.0 

.5619 

.9843 

.3 

40' 

.4430 

4.9 

.5570 

.9839 

.4 

30' 

.4479 

4.9 

.5521 

.9836 

.3 

20' 

.4527 

4.8 

4.8 

4.7 

.5473 

.9832 

.4 

.4 

.3 

10' 

9.4575 

10.5425 

9.9828 

o 

O 

.4622 

.5378 

.9825 

50' 

.4669 

4.7 

.5331 

.9821 

.4 

40' 

.4716 

4.7 

.5284 

.9817 

.4 

30' 

.4762 

4.6 

.5238 

.9814 

.3 

20' 

.4808 

4.6 

4.5 

4.5 

.5192 

.9810 

.4 

.4 

.4 

.4 

10' 

9.4853 

10.5147 

9.9806 

73° 0' 

.4898 

.5102 

.9802 

50' 

.4943 

4.5 

.5057 

.9798 

40' 

.4987 ' 

4.4 

.5013 

• .9794 

.4 

30' 

.5031 1 

4.4 

.4969 

.9790 

.4 

20' 

.5075 

4.4 

4.3 

4.3 

.4925 

.9786 

.4 

.4 

.4 

.4 

10' 

9.5118 

10.4882 

9.9782 

o 

o 

.5161 

.4839 

.9778 

50' 

.5203 

4.2 

.4797 

.9774 

40' 

.5245 

4.2 

.4755 

.9770 

.4 

30' 

.5287 

4.2 

.4713 

.9765 

.5 

20' 

.5329 

4.2 

4.1 

4.1 

4.0 

.4671 

.9761 

.4 

.4 

.5 

.4 

10' 

9.5370 

10.4630 

9.9757 

71° 0' 

.5411 

.4589 

.9752 

50' 

.5451 

.4549 

.9748 

40' 

.5491 

4.0 

.4509 

.9743 

.5 

30' 

.5531 

4.0 

.4469 

.9739 

.4 

20' 

.5571 

4.0 

4.0 

3.9 

.4429 

.9734 

.5 

.4 

.5 

.4 

10' 

9.5611 

10.4389 

9.9730 

o 

o 

O 

.5650 

.4350 

.9725 

50' 

.5689 

3.9 

.4311 

.9721 

40' 

.5727 

3.8 

.4273 

.9716 

.5 

30' 

.5766 

3.9 

.4234 

.9711 

.5 

20' 

.5804 

3.8 

3.8 

.4196 

.9706 

.5 

.4 

10' 

9.5842 

10.4158 

9.9702 

69° 0' 

L Cot 

c d 1' 

L Tan 

L Sin 

dl' 

Angle 






























































































IV 


FOUR-PLACE LOGARITHMS OF FUNCTIONS 


15 


Angle 


21 ° 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

22 ° 0 ' 

10 ' 

20 ' 

30' 

40' 

50' 

23° 0' 

10 ' 
20 ' 
30' 
40' 
50' 
24° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

25° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

26° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

27° 0' 

10 ' 

20 ' 

30' 

40' 

50' 

28°- 0' 

10 ' 

20 ' 

30' 

40' 

50' 

29° 0' 


L Sin I d 1' 


9.5543 


.5576 

.5609 

.5641 

.5673 

.5704 

9.5736 

.5767 

.5798 

.5828 

.5859 

.5889 

9.5919 

.5948 

.5978 

.6007 

.6036 

.6065 

9.6093 

.6121 

.6149 

.6177 

.6205 

.6232 

9.6259 

.6286 

.6313 

.6340 

.6366 

.6392 

9.6418 

.6444 

.6470 

.6495 

.6521 

.6546 

9.6570 

.6595 

.6620 

.6644 

.6668 

.6692 

9.6716 

.6740 

.6763 

.6787 

.6810 

.6833 


9.6856. 


3.3 

3.3 
3.2 
3.2 

3.1 

3.2 

3.1 

3.1 

3.0 

3.1 

3.0 

3.0 

2.9 

3.0 

2.9 

2.9 

2.9 

2.8 

2.8 

2.8 

2.8 

2.8 

2.7 

2.7 

2.7 

2.7 

2.7 

2.6 

2.6 

2.6 

2.6 

2.6 

2.5 

2.6 

2.5 

2.4 

2.5 

2.5 

2.4 

2.4 

2.4 

2.4 

2.4 

2.3 

2.4 
2.3 
2.3 
2.3 


L Tan c d 1' 


L Cot 


9.5842 


.5879 

.5917 

.5954 

.5991 

.6028 

9.6064 

.6100 

.6136 

.6172 

.6208 

.6243 

9.6279 

.6314 

.6348 

.6383 

.6417 

.6452 

9.6486 

.6520 

.6553 

.6587 

.6620 

.6654 

9.6687 

.6720 

.6752 

.6785 

.6817 

.6850 

9.6882 

.6914 

.6946 

.6977 

.7009 

.7040 

9.7072 

.7103 

.7134 

.7165 

.7196 

.7226 

9.7257 

.7287 

.7317 

.7348 

.7378 

.7408 

9.7438 


L Cos d 1' 


3.7 

3.8 
3.7 
3.7 
3.7 
3.6 

3.6 

3.6 

3.6 

3.6 

3.5 

3.6 

3.5 

3.4 

3.5 

3.4 

3.5 
3.4 

3.4 

3.3 

3.4 

3.3 

3.4 
3.3 

3.3 

3.2 

3.3 

3.2 

3.3 
3.2 

3.2 

3.2 

3.1 

3.2 

3.1 

3.2 

3.1 

3.1 

3.1 

3.1 

3.0 

3.1 

3.0 

3.0 

3.1 

3.0 

3.0 

3.0 


10.4158 


.4121 

.4083 

.4046 

.4009 

.3972 


10.3936 


.3900 

.3864 

.3828 

.3792 

.3757 


10.3721 


.3686 

.3652 

.3617 

.3583 

.3548 


10.3514 


.3480 

.3447 

.3413 

.3380 

.3346 


10.3313 


L Cot i c d 1' 


.3280 

.3248 

..3215 

.3183 

.3150 


10.3118 


.3086 

.3054 

.3023 

.2991 

.2960 


10.2928 


.2897 

.2866 

.2835 

.2804 

.2774 


10.2743 


.2713 

.2683 

.2652 

.2622 

.2592 


10.2562 


L Tan 


L Cos 


9.9702 


.9697 

.9692 

.9687 

.9682 

.9677 


9.9672 


.9667 

.9661 

.9656 

.9651 

.9646 


9.9640 


.9635 

.9629 

.9624 

.9618 

.9613 


9.9607 


.9602 

.9596 

.9590 

.9584 

.9579 


9.9573 


.9567 

.9561 

.9555 

.9549 

.9543 


9.9537 


.9530 

.9524 

.9518 

.9512 

.9505 


9.9499 


.9492 

.9486 

.9479 

.9473 

.9466 


9.9459 


.9453 

.9446 

.9439 

.9432 

.9425 


9.9418 


L Sin 


d 1' 


d 1' 


69° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

68 ° 0 ' 

50' 

40' 

30' 

20 ' 

10 ' 

67° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

66 ° 0 ' 

50' 

40' 

30' 

20 ' 

10 ' 

65° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

64° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

63° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

62° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

61° 0' 


Angle 
























































































16 


FOUR-PLACE LOGARITHMS OF FUNCTIONS 


IV 


Angle 


L Sin 


29° 0' 

9.6856 

2.2 

10' 

.6878 

20' 

.6901 

2.3 

30' 

.6923 

2.2 

40' 

.6946 

2.3 

50' 

.6968 

2.2 

2.2 

2.2 

b 

o 

O 

CO 

9.6990 



10' 

.7012 

2.1 

20' 

.7033 

30' 

.7055 

2.2 

40' 

.7076 

2.1 

50' 

.7097 

2.1 

2.1 

2.1 

31° 0' 

9.7118 

10' 

.7139 

20' 

.7160 

2.1 

30' 

.7181 

2.1 

40' 

.7201 

2.0 

50' 

.7222 

2.1 

2.0 

2.0 

32° 0' 

9.7242 

10' 

.7262 

20' 

.7282 

2.0 

30' 

.7302 

2.0 

40' 

.7322 

2.0 

50' 

.7342 

2.0 

1.9 

1.9 

33° 0' 

9.7361 

10' 

.7380 

20' 

.7400 

2.0 

30' 

.7419 

1.9 

40' 

.7438 

1.9 

50' 

.7457 

1.9 

1.9 

1.8 

34° 0' 

9.7476 

10' 

.7494 

20' 

.7513 

1.9 

30' 

.7531 

1.8 

40' 

.7550 

1.9 

50' 

.7568 

1.8 

1.8 

1.8 

35° 0' 

9.7586 

10' 

.7604 

20' 

.7622 

1.8 

30' 

.7640 

1.8 

40' 

.7657 

1.7 

50' 

.7675 

1.8 

1.7 

1.8 

36° 0' 

9.7692 

10' 

.7710 

20' 

.7727 

1.7 

30' 

.7744 

1.7 

40' 

.7761 

1.7 

50' 

.7778 

1.7 

1.7 

b 

o 

l> 

CO 

9.7795 


L Cos 

dl' 


d 1 ' 


L Tan 


9.7438 

.7467 

.7497 

.7526 

.7556 

.7585 

9.7614 

.7644 

.7673 

.7701 

.7730 

.7759 

9.7788 

.7816 

.7845 

.7873 

.7902 

.7930 

9.7958 

.7986 

.8014 

.8042 

.8070 

.8097 

9.8125 

.8153 

.8180 

.8208 

.8235 

.8263 

9.8290 

.8317 

.8344 

.8371 

.8398 

.8425 

9.8452 

.8479 

.8506 

.8533 

.8559 

.8586 

9.8613 

.8639 

.8666 

.8692 

.8718 

.8745 

9.8771 

L Cot 


c d 


2.9 

3.0 

2.9 

3.0 

2.9 

2.9 

3.0 

2.9 

2.8 

2.9 

2.9 

2.9 

2.8 

2.9 

2.8 

2.9 

2.8 

2.8 

2.8 

2.8 

2.8 

2.8 

2.7 

2.8 

2.8 

2.7 

2.8 

2.7 

2.8 

2.7 

2.7 

2.7 

2.7 

2.7 

2.7 

2.7 

2.7 

2.7 

2.7 

2.6 

2.7 

2.7 

2.6 

2.7 

2.6 

2.6 

2.7 

2.6 


c d 1' 


L Cot 


10.2562 

.2533 

.2503 

.2474 

.2444 

.2415 

10.2386 

.2356 

.2327 

.2299 

.2270 

.2241 

10.2212 

.2184 

.2155 

.2127 

.2098 

.2070 

10.2042 

.2014 

.1986 

.1958 

.1930 

.1903 

10.1875 

.1847 

.1820 

.1792 

.1765 

.1737 

10.1710 

.1683 

.1656 

.1629 

.1602 

.1575 

10.1548 

.1521 

.1494 

.1467 

.1441 

.1414 

10.1387 

.1361 

.1334 

.1308 

.1282 

.1255 

10.1229 

L Tan 


L Cos 


9.9418 


.9411 

.9404 

.9397 

.9390 

.9383 


9.9375 


.9368 

.9361 

.9353 

.9346 

.9338 


9.9331 


.9323 

.9315 

.9308 

.9300 

.9292 


9.9284 


.9276 

.9268 

.9260 

.9252 

.9244 


9.9236 


.9228 

.9219 

.9211 

.9203 

.9194 


9.9186 


.9177 

.9169 

.9160 

.9151 

.9142 


9.9134 


.9125 

.9116 

.9107 

.9098 

.9089 


9.9080 


.9070 

.9061 

.9052 

.9042 

.9033 


9.9023 


L Sin 


d 1' 


.7 

.7 

.7 

.7 

.7 

.8 

.7 

.7 

.8 

.7 

.8 

.7 

.8 

.8 

.7 

.8 

.8 

.8 


.8 

.8 

.8 

.8 

.8 

.9 

.8 

.8 

.9 

.8 

.9 

.8 

.9 

.9 

.9 

.8 

.9 

.9 

.9 

.9 

.9 

.9 

1.0 

.9 

.9 

1.0 

.9 

1.0 


dl' 


61° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

60° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

59° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

58° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

57° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

56° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

55° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

54° 0' 

50' 

40' 

30' 

20 ' 

10 ' 

53° 0' 


Angle 





















































































IV 


FOUR-PLACE LOGARITHMS OF FUNCTIONS 


17 


Angle 


37° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

38° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

39° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

40° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

41° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

42° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

43° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

44° 0' 

10 ' 

20 ' 

30 ' 

40 ' 

50 ' 

45° 0' 


L Sin 

9.7795 

.7811 

.7828 

.7844 

.7861 

.7877 

9.7893 

.7910 

.7926 

.7941 

.7957 

.7973 

9.7989 

.8004 

.8020 

.8035 

.8050 

.8066 

9.8081 

.8096 

.8111 

.8125 

.8140 

.8155 

9.8169 

.8184 

.8198 

.8213 

.8227 

.8241 

9.-8255 

.8269 

.8283 

.8297 

.8311 

.8324 

9.8338 

.8351 

.8365 

.8378 

.8391 

.8405 

9.8418 

.8431 

.8444 

.8457 

.8469 

.8482 

9.8495 

L Cos 


d 1' 


1.6 

1.7 

1.6 

1.7 

1.6 

1.6 

1.7 

1.6 

1.5 

1.6 
1.6 
1.6 

1.5 

1.6 
1.5 

1.5 

1.6 
1.5 

1.5 

1.5 

1.4 

1.5 
1.5 

1.4 

1.5 

1.4 

1.5 
1.4 
1.4 
1.4 

1.4 

1.4 

1.4 

1.4 

1.3 

1.4 

1.3 

1.4 
1.3 

1.3 

1.4 
1.3 

1.3 

1.3 

1.3 

1.2 

1.3 

1.3 


dl' 


L Tan 

c d 1' 

L Cot 

L Cos 

dl' 


9.8771 

2.6 

10.1229 

9.9023 

.9 

53° 0' 

.8797 

.1203 

.9014 

50' 

.8824 

2.7 

.1176 

.9004 

1.0 

40 ' 

.8850 

2.6 

.1150 

.8995 

.9 

30 ' 

.8876 

2.6 

.1124 

.8985 

1.0 

20 ' 

.8902 

2.6 

2.6 

2.6 

2.6 

.1098 

.8975 

1.0 

1.0 

1.0 

1.0 

10 ' 

9.8928 

10.1072 

9.8965 

52° 0' 

.8954 

.1046 

.8955 

50' 

.8980 

.1020 

.8945 

40 ' 

.9006 

2.6 

.0994 

.8935 

1.0 

30 ' 

.9032 

2.6 

.0968 

.8925 

1.0 

20 ' 

.9058 

2.6 

2.6 

2.6 

2.5 

.0942 

.8915 

1.0 

1.0 

1.0 

1.1 

10 ' 

9.9084 

10.0916 

9.8905 

51° 0' 

.9110 

.0890 

.8895 

50 ' 

.9135 

.0865 

.8884 

40 ' 

.9161 

2.6 

.0839 

.8874 

1.0 

30 ' 

.9187 

2.6 

.0813 

.8864 

1.0 

20 ' 

.9212 

2.5 

2.6 

2.6 

.0788 

.8853 

1.1 

1.0 

1.1 

10 ' 

9.9238 

10.0762 

9.8843 

50° 0' 

.9264 

.0736 

.8832 

50 ' 

.9289 

2.5 

.0711 

.8821 

1.1 

40 ' 

.9315 

2.6 

.0685 

.8810 

1.1 

30 ' 

.9341 

2.6 

.0659 

.8800 

1.0 

20 ' 

.9366 

2.5 

2.6 

2.5 

.0634 

.8789 

1.1 

1.1 

1.1 

10 ' 

9.9392 

10.0608 

9.8778 

49° 0' 

.9417 

.0583 

.8767 

50 ' 

.9443 

2.6 

.0557 

.8756 

1.1 

40 ' 

.9468 

2.5 

.0532 

.8745 

1.1 

30 ' 

.9494 

2.6 

.0506 

.8733 

1.2 

1.1 

1.1 

1.2 

1.1 

20 ' 

.9519 

2.5 

2.5 

2.6 

.0481 

.8722 

10 ' 

9.9544 

10.0456 

9.8711 

48° 0' 

.9570 

.0430 

.8699 

50 ' 

.9595 

2.5 

.0405 

.8688 

40 ' 

.9621 

2.6 

.0379 

.8676 

1.2 

30 ' 

.9646 

2.5 

.0354 

.8665 

1.1 

20 ' 

.9671 

2.5 

2.6 

2.5 

.0329 

.8653 

1.2 

1.2 

1.2 

1.1 

10 ' 

9.9697 

10.0303 

9.8641 

47° 0' 

.9722 

.0278 

.8629 

50 ' 

.9747 

2.5 

.0253 

.8618 

40 ' 

.9772 

2.5 

.0228 

.8606 

1.2 

30 ' 

.9798 

2.6 

.0202 

.8594 

1.2 

20 ' 

.9823 

2.5 

2.5 

2.6 

2.5 

.0177 

.8582 

1.2 

1.3 

1.2 

1.2 

10 ' 

9.9848 

1 10.0152 

9.8569 

46° 0' 

.9874 

.0126 

.8557 

50 ' 

.9899 

.0101 

.8545 

40 ' 

.9924 

2.5 

.0076 

.8532 

1.3 

30 ' 

.9949 

2.5 

.0051 

.8520 

1.2 

20 ' 

.9975 

2.6 

O K 

.0025 

.8507 

1.3 

1.2 

10 ' 

10.0000 


i 10.0000 

9.8495 

45° 0' 

L Cot 

c d 1' 

L Tan 

L Sin 

d 1' 

Angle 








































































































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TABLE V 


FIVE-PLACE LOGARITHMS 
OF THE 

TRIGONOMETRIC FUNCTIONS 
OF 

ANGLES BETWEEN 0° AND 3° 
AND BETWEEN 87° AND 90° 


Note. — For angles between 0° and 3° and between 87° and 90° Table Va or Table Yb may 
be used to avoid interpolation in Table IV or in ordinary five-place tables; the results thus 
obtained are more accurate. Errors of interpolation in Table Yb correspond to differences 
of angle of less than 1" ; Table Ya gives still more accurate results. 


Va. AUXILIARY TABLE OF S AND T FOR A IN MINUTES 

For angles near 0°: log sin A = S + log A' and log tan A = T A log A'. 

For angles near 90°: log cos d. = Si -|- log A'l and log cot A = Ti + log A'l where A'l 

is the number of minutes in 90° — A and Si and Ti are corresponding values of S and T. 


A' 

S + 10 


A’ 

T + 10 

A' 

r + 10 

0' - 13' 

6.46 373 


0' - 26' 

6.46 373 

131' - 133' 

6.46 394 

14' - 42' 

372 


27' - 39' 

374 

134' - 136' 

395 

43' - 58' 

371 


40' - 48' 

375 

137' - 139' 

396 

59' - 71' 

6.46 370 


49' - 56' 

6.46 376 

140' - 142' 

6.46 397 

72' - 81' 

369 


57' - 63' 

377 

143' - 145' 

398 

82' - 91' 

368 


64' - 69' 

378 

146' - 148' 

399 

92' - 99' 

6.46 367 


70' - 74' 

6.46 379 

149' - 150' 

6.46 400 

100' - 107' 

366 


75' - 80' 

380 

151' - 153' 

401 

108' - 115' 

365 


81' - 85' 

381 

154' - 156' 

402 

116' - 121' 

6.46 364 


86' - 89' 

6.46 382 

157' - 158' 

6.46 403 

122' - 128' 

363 


90' - 94' 

383 

159' - 161' 

404 

129' - 134' 

362 


95' - 98' 

384 

162' - 163' 

405 

135' - 140' 

6.46 361 


99' - 102' 

6.46 385 

164' - 166' 

6.46 406 

141' - 146' 

360 


103' - 106' 

386 

167' - 168' 

407 

147' - 151' 

359 


107' - 110' 

387 

169' - 171' 

408 

152' - 157' 

6.46 358 


111' - 113' 

6.46 388 

172' - 173' 

6.46 409 

158' - 162' 

357 


114' - 117' 

389 

174' - 175' 

410 

163' - 167' 

356 


118' - 120' 

390 

176' - 178' 

411 

168' - 171' 

6.46 355 


121' - 124' 

6.46 391 

179' - 180' 

6.46 412 

172' - 176' 

354 


125' - 127' 

392 

181' - 182' 

413 

177' - 181' 

353 


128' - 130' 

393 

183' - 184' 

414 


21 












22 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


Vb 


ANGLES NEAR 0° AND 90° 


Angle 

Log Sin A + 10 

C 


A 

0" 

10" 

20" 

30" 

40" 

60" 

.0000 


0° 0' 


5.68 557 

5.98 660 

6.16 270 

6.28 763 

6.38 454 

0 


1' 

6.46 373 

6.53 067 

6.58 866 

6.63 982 

6.68 557 

6.72 697 

0 

O ^ 

2' 

6.76 476 

6.79 952 

6.83 170 

6.86 167 

6.88 969 

6.91 602 

0 

3' 

6.94 085 

6.96 433 

6.98 660 

7.00 779 

7.02 800 

7.04 730 

0 


4' 

7.06 579 

7.08 351 

7.10 055 

7.11 694 

7.13 273 

7.14 797 

0 

go 

5' 

7.16 270 

7.17 694 

7.19 072 

7.20 409 

7.21 705 

7.22 964 

0 

S 

6' 

7.24 188 

7.25 378 

7.26 536 

7.27 664 

7.28 763 

7.29 836 

0 

o¥ 

7' 

7.30 882 

7.31 904 

7.32 903 

7.33 879 

7.34 833 

7.35 767 

0 

i-H O 

8' 

7.36 682 

7.37 577 

7.38 454 

7.39 314 

7.40 158 

7.40 985 

0 

1 II 

9' 

7.41 797 

7.42 594 

7.43 376 

7.44 145 

7.44 900 

7.45 643 

0 

005 

0° 10' 

7.46 373 

7.47 090 

7.47 797 

7.48 491 

7.49 175 

7.49 849 

0 

1.2 

11' 

7.50 512 

7.51 165 

7.51 808 

7.52 442 

7.53 067 

7.53 683 

0 

OCQ 

12' 

7.54 291 

7.54 890 

7.55 481 

7.56 064 

7.56 639 

7.57 206 

0 


13' 

7.57 767 

7.58 320 

7.58 866 

7.59 406 

7.59 939 

7.60 465 

0 

II g 

14' 

7.60 985 

7.61 499 

7.62 007 

7.62 509 

7.63 006 

7.63 496 

1 

•^.2 

15' 

7.63 982 

7.64 461 

7.64 936 

7.65 406 

7.65 870 

7.66 330 

1 

si 

16' 

7.66 784 

7.67 235 

7.67 680 

7.68 121 

7.68 557 

7.68 989 

1 


17' 

7.69 417 

7.69 841 

7.70 261 

7.70 676 

7.71088 

7.71 496 

1 


18' 

7.71 900 

7.72 300 

7.72 697 

7.73 090 

7.73 479 

7.73 865 

1 


19' 

7.74 248 

7.74 627 

7.75 003 

7.75 376 

7.75 745 

7.76 112 

1 

o 

oS 
. 0 

0° 20' 

7.76 475 

7.76 836 

7.77 193 

7.77 548 

7.77 899 

7.78 248 

1 

21' 

7.78 594 

7.78 938 

7.79 278 

7.79 616 

7.79 952 

7.80 284 

1 

O 

05 

22' 

7.80 615 

7.80 942 

7.81 268 

7.81 591 

7.81 911 

7.82 229 

1 


23' 

7.82 545 

7.82 859 

7.83 170 

7.83 479 

7.83 786 

7.84 091 

1 

a 2 

24' 

7.84 393 

7.84 694 

7.84 992 

7.85 289 

7.85 583 

7.85 876 

1 

C3 

25' 

7.86 166 

7.86 455 

7.86 741 

7.87 026 

7.87 309 

7.87 590 

1 

h-i a , 

26' 

7.87 870 

7.88 147 

7.88 423 

7.88 697 

7.88 969 

7.89 240 

1 

27' 

7.89 509 

7.89 776 

7.90 041 

7.90 305 

7.90 568 

7.90 829 

1 

1 ^ ' 

28' 

7.91 088 

7.91 346 

7.91 602 

7.91 857 

7.92 110 

7.92 362 

1 

te O 

o -20 

.-1 4) 05 

29' 

7.92 612 

7.92 861 

7.93 108 

7.93 354 

7.93 599 

7.93 842 

2 

0° 30' 

7.94 084 

7.94 325 

7.94 564 

7.94 802 

7.95 039 

7.95 274 

2 

II 

31' 

7.95 508 

7.95 741 

7.95 973 

7.96 203 

7.96 432 

7.96 660 

2 

^ CQ 

fl 11 

O g5 

32' 

7.96 887 

7.97 113 

7.97 337 

7.97 560 

7.97 782 

7.98 003 

2 

33' 

7.98 223 

7.98 442 

7.98 660 

7.98 876 

7.99 092 

7.99 306 

2 


34' 

7.99 520 

7.99 732 

7.99 943 

8.00 154 

8.00 363 

8.00 571 

2 


35' 

8.00 779 

8.00 985 

8.01 190 

8.01 395 

8.01 598 

8.01 801 

2 

M fl O 

36' 

8.02 002 

8.02 203 

8.02 402 

8.02 601 

8.02 799 

8.02 996 

2 

••‘.2 

37' 

8.03 192 i 

8.03 387 

8.03 581 

8.03 775 

8.03 967 

8.04 159 

3 


38' 

8.04 350 

8.04 540 

8.04 729 

8.04 918 

8.05 105 

8.05 292 

3 

■^<2 1 

39' 

8.05 478 

8.05 663 

8.05 848 

8.06 031 

8.06 214 

8.06 396 

3 


0° 40' 

8.06 578 

8.06 758 

8.06 938 

8.07 117 

8.07 295 

8.07 473 

3 

41' 

8.07 650 

8.07 826 

8.08 002 

8.08 176 

8.08 350 

8.08 524 

3 

M . 0 

42' 

8.08 696 

8.08 868 

8.09 040 

8.09 210 

8.09 380 

8.09 550 

4 


43' 

8.09 718 

8.09 886 

8.10 054 

8.10 220 

8.10 386 

8.10 552 

4 

II 2 II 

44' 

8.10 717 

8.10 881 

8.11 044 

8.11 207 

8.11 370 

8.11 531 

4 

II a II 

45' 

8.11 693 

8.11 853 

8.12 013 

8.12 172 

8.12 331 

8.12 489 

4 

^^«i 

i=i2-s 

H 0 

46' 

8.12 647 

8.12 804 

8.12 961 

8.13 117 

8.13 272 

8.13 427 

4 

47' 

8.13 581 

8.13 735 

8.13 888 

8.14 041 

8.14 193 

8.14 344 

4 


48' 

8.14 495 

8.14 646 

8.14 796 

8.14 945 

8.15 094 

8.15 243 

4 


49' 

8.15 391 

8.15 538 

8.15 685 

8.15 832 

8.15 978 

8.16 123 

4 


0°60' 

8.16 268 

8.16 413 

8.16 557 

8.16 700 

8.16 843 

8.16 986 

5 

1 

51' 

8.17 128 

8.17 270 

8.17 411 

8.17 552 

8.17 692 

8.17 832 

5 


52' 

8.17 971 

8.18 110 

8.18 249 

8.18 387 

8.18 524 

8.18 662 

5 

doS 

53' 

8.18 798 

8.18 935 

8.19 071 

8.19 206 

8.19 341 

8.19 476 

5 

^ Jh 

0 . (h ^ 

54' 

8.19 610 

8.19 744 

8.19 877 

8.20 010 

8.20 143 

8.20 275 

6 

1 o S 

55' 

8.20 407 

8.-20 538 

8.20 669 

8.20 800 

8.20 930 

8.21 060 

6 

II 

CQ a Cl 

56' 

8.21 189 

8.21 319 

8.21 447 

8.21 576 

8.21 703 

8.21 831 

6 

57' 

8.21 958 

8.22 085 

8.22 211 

8.22 337 

8.22 463 

8.22 588 

6 

58' 

8.22 713 

8.22 838 

8.22 962 

8.23 086 

8.23 210 

8.23 333 

6 

032 

59' 

8.23 456 

8.23 578 

8.23 700 

8.23 822 : 

8.23 944 

8.24 065 

6 



















































Vb 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


23 


ANGLES NEAR 0° AND 90° 


Angle 

Log Sin i4 4- 10 

C 


A 

0" 

10" 

20" 

30" 

40" 

60" 

.0000 


1° 0' 

8.24 186 

8.24 306 

8.24 426 

8.24 546 

8.24 665 

8.24 785 

7 


1' 

8.24 903 

8.25 022 

8.25 140 

8.25 258 

8.25 375 

8.25 493 

7 


2' 

8.25 609 

8.25 726 

8.25 842 

8.25 958 

8.26 074 

8.26 189 

7 


3' 

8.26 304 

8.26 419 

8.26 533 

8.26 648 

8.26 761 

8.26 875 

7 

0. 1 
a; ' 

4' 

8.26 988 

8.27 101 

8.27 214 

8.27 326 

8.27 438 

8.27 550 

8 

K o 

5' 

8.27 661 

8.27 773 

8.27 883 

8.27 994 

8.28 104 

8.28 215 

8 

© 

6' 

8.28 324 

8.28 434 

8.28 543 

8.28 652 

8.28 761 

8.28 869 

8 

o'i 

7' 

8.28 977 

8.29 085 

8.29 193 

8.29 300 

8.29 407 

8.29 514 

9 

i-H O 

8' 

8.29 621 

8.29 727 

8.29 833 

8.29 939 

8.30 044 

8.30 150 

9 

1 11 

9' 

8.30 255 

8.30 359 

8.30 464 

8.30 568 

8.30 672 

8.30 776 

9 

Ocq 

b 

o 

v-l 

8.30 879 

8.30 983 

8.31 086 

8.31 188 

8.31 291 

8.31 393 

9 

1 a 

11' 

8.31 495 

8.31 597 

8.31 699 

8.31 800 

8.31 901 

8.32 002 

9 

o’” 

12' 

8.32 103 

8.32 203 

8.32 303 

8.32 403 

8.32 503 

8.32 602 

.00010 

II S2 

13' 

8.32 702 

8.32 801 

8.32 899 

8.32 998 

8.33 096 

8.33 195 

10 

_ o 

14' 

8.33 292 

8.33 390 

8.33 488 

8.33 585 

8.33 682 

8.33 779 

10 


15' 

8.33 875 

8.33 972 

8.34 068 

8.34 164 

8.34 260 

8.34 355 

10 

Ei 

16' 

8.34 450 

8.34 546 

8.34 640 

8.34 735 

8.34 830 

8.34 924 

11 

o S 

17' 

8.35 018 

8.35 112 

8.35 206 

8.35 299 

8.35 392 

8.35 485 

11 


18' 

8.35 578 

8.35 671 

8.35 764 

8.35 856 

8.35 948 

8.36 040 

11 


19' 

8.36 131 

8.36 223 

8.36 314 

8.36 405 

8.36 496 

8.36 587 

12 

o B 

1° 20' 

8.36 678 

8.36 768 

8.36 858 

8.36 948 

8.37 03^..^ 

"8.37 128 

12 

^ o 

1 O 

21' 

8.37 217 

8.37 306 

8.37 395 

8.37 484 

8.37 573 

8.37 662 

12 

1 ^ 

22' 

8.37 750 

8.37 838 

8.37 926 

8.38 014 

8.38 101 

8.38 189 

12 


23' 

8.38 276 

8.38 363 

8.38 450 

8.38 537 

8.38 624 

8.38 710 

13 

c § 

24' 

8.38 796 

8.38 882 

8.38 968 

8.39 054 

8.39 139 

8.39 225 

13 

So 

•+^1^ • 

25' 

8.39 310 

8.39 395 

8.39 480 

8.39 565 

8.39 649 

8.39 734 

13 


26' 

8.39 818 

8.39 902 

8.39 986 

. 8.40 070 

8.40 153 

8.40 237 

14 

1 

27' 

8.40 320 

8.40 403 

8.40 486 ' 

8.40 569 

8.40 651 

8.40 734 

14 

1 io 

28' 

8.40 816 

8.40 898 

8.40 980 

8.41 062 

8.41 144 

8.41 225 

15 

.So 

29' 

8.41 307 

8.41 388 

8.41 469 

8.41 550 

8.41 631 

8.41 711 

15 

2^© 

1° 30' 

8.41 792 

8.41 872 

8.41 952 

8.42 032 

8.42 112 

8.42 192 

15 

II oQ d 

31' 

8.42 272 

8.42 351 

8.42 430 

8.42 510 

8.42 589 

8.42 667 

15 

^ II 

32' 

8.42 746 

8.42 825 

8.42 903 

8.42 982 

8.43 060 

8.43 138 

16 

o 

33' 

8.43 216 

8.43 293 

8.43 371 

8.43 448 

8.43 526 

8.43 603 

16 


34' 

8.43 680 

8.43 757 

8.43 834 

8.43 910 

8.43 987 

8.44 063 

16 

M ° 

O 2 S 

35' 

8.44 139 

8.44 216 

8.44 292 

8.44 367 

8.44 443 

8.44 519 

17 

"^.2 - 

36' 

8.44 594 

8.44 669 

8.44 745 

8.44 820 

8.44 895 

8.44 969 

17 


37' 

8.45 044 

8.45 119 

8.45 193 

8.45 267 

8.45 341 

8.45 415 

17 

o|^ 

38' 

8.45 489 

8.45 563 

8.45 637 

8.45 710 

8.45 784 

8.45 857 

18 

+2 1 

39' 

8.45 930 

8.46 003 

8.46 076 

8.46 149 

8.46 222 

8.46 294 

18 

O O 

1° 40' 

8.46 366 

8.46 439 

8.46 511 

8.46 583 

8.46 655 

8.46 727 

18 

02 

41' 

8.46 799 

8.46 870 

8.46 942 

8.47 013 

8.47 084 

8.47 155 

19 

hC . 3 

42' 

8.47 226 

8.47 297 

8.47 368 

8.47 439 

8.47 509 

8.47 580 

19 

o Cl 
j c 

43' 

8.47 650 

8.47 720 

8.47 790 

8.47 860 

8.47 930 

8.48 000 

20 

II 4 II 

44' 

8.48 069 

8.48 139 

8.48 208 

8.48 278 

8.48 347 

8.48 416 

20 

11 Pi 1 

45' 

8.48 485 

8.48 554 

8.48 622 

8.48 691 

8.48 760 

8.48 828 

20 


46' 

8.48 896 

8.48 965 

8.49 033 

8.49 101 

8.49 169 

8.49 236 

20 

O 

o3 U 

47' 

8.49 304 

8.49 372 

8.49 439 

8.49 506 

8.49 574 

8.49 641 

21 


48' 

8.49 708 

8.49 775 

8.49 842 

8.49 908 

8.49 975 

8.50 042 

21 

b£!4^^ 

O r* PO 

49' 

8.50 108 

8.50 174 

8.50 241 

8.50 307 

8.50 373 

8.50 439 

22 


1° 50' 

8.50 504 

8.50 570 

8.50 636 

8.50 701 

8.50 767 

8.50 832 

23 


51' 

8.50 897 

8.50 963 

8.51 028 

8.51 092 

8.51 157 

8.51 222 

23 

(M *^0 

52' 

8.51 287 

8.51 351 

8.51 416 

8.51 480 

8.51 544 

8.51 609 

23 


53' 

8.51 673 

8.51 737 

8.51 801 

8.51 864 

8.51 928 

8.51 992 

23 

o QJ O 

54' 

8.52 055 

8.52 119 

8.52 182 

8.52 245 

8.52 308 

8.52 371 

24 


55' 

8.52 434 

8.52 497 

8.52 560 

8.52 623 

8.52 685 

8.52 748 

24 

^2 II 

56' 

8.52 810 

8.52 872 

8.52 935 

8.52 997 

8.53 059 

8.53 121 

25 


57' 

8.53 183 

8.53 245 

8.53 306 

8.53 368 

8.53 429 

8.53 491 

25 

M ad 

58' 

8.53 552 

8.53 614 

8.53 675 

8.53 736 

8.53 797 

8.53 858 

26 

c3 2 

59' 

8.53 919 

8.53 979 

8.54 040 

8.54 101 

8.54 161 

8:54 222 

26 


























































24 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


V6 


ANGLES NEAR 0° AND 90° 


Angle 





Log Sin 

A + 

10 



C 


A 

0" 

10" 

2( 


30" 

40" 

! 50" 

.000 


2° 0' 

8.54 

282 

8.54 

342 

8.54 

402 

8.54 

462 

8.54 522 

8.54 582 

27 


1 ' 

8.54 

642 

8.54 

702 

8.54 

762 

8.54 

821 

8.54 881 

8.54 940 

27 


2 ' 

8.54 

999 

8.55 

059 

8.55 

118 

8.55 

177 

8.55 236 

8.55 295 

28 


3 ' 

8.55 

354 

8.55 

413 

8.55 

471 

8.55 

530 

8.55 589 

8.55 647 

28 

p . 1 

4 ' 

8.55 

705 

8.55 

764 

8.55 

822 

8.55 

880 

8.55 938 

8.55 996 

29 

oo 
!«! O 

5 ' 

8.56 

054 

8.56 

112 

8.56 

170 

8.56 

227 

8.56 285 

8.56 342 

29 

(DO 

6' 

8.56 

400 

8.56 

457 

8.56 

515 

8.56 

572 

8.56 629 

8.56 686 

29 

o S 

r 

8.56 

743 

8.56 

800 

8.56 

857 

8.56 

914 

8.56 970 

8.57 027 

30 

W Q 

8 ' 

8.57 

084 

8.57 

140 

8.57 

196 

8.57 

253 

8.57 309 

8.57 365 

30 

1 II 

9 ' 

8.57 

421 

8.57 

477 

8.57 

533 

8.57 

589 

8.57 645 

8.57 701 

31 

Ocq 

b 

o 

8.57 

757 

8.57 

812 

8.57 

868 

8.57 

927 

8.57 979 

8.58 034 

31 

1 P 

11 ' 

8.58 

089 

8.58 

144 

8.58 

200 

8.58 

255 

8.58 310 

8.58 364 

32 

o 

12 ' 

8.58 

419 

8.58 

474 

8.58 

529 

8.58 

583 

8.58 638 

8.58 693 

32 


13 ' 

8.58 

747 

8.58 

801 

8.58 

856 

8.58 

910 

8.58 964 

8.59 018 

33 

a 

14 ' 

8.59 

072 

8.59 

126 

8.59 

180 

8.59 

234 

8.59 288 

8.59 341 

33 


15 ' 

8.59 

395 

8.59 

448 

8.59 

502 

8.59 

555 

8.59 609 

8.59 662 

34 

oo o3 

O -t! 

16 ' 

8.59 

715 

8.59 

768 

8.59 

821 

8.59 

874 

8.59 927 

8.59 980 

35 

y D 

17 ' 

8.60 

033 

8.60 

086 

8.60 

139 

8.60 

191 

8.60 244 

8.60 296 

35 


18 ' 

8.60 

349 

8.60 

401 

8.60 

454 

8.60 

506 

8.60 558 

8.60 610 

35 

1-^73 

19 ' 

8.60 

662 

8.60 

714 

8.60 

766 

8.60 

818 

8.60 870 

8.60 922 

36 

o g 

2° 20' 

8.60 

973 

8.61 

025 

8.61 

077 

8.61 

128 

8.61 180 

8.61 231 

36 

7?-, 

21 ' 

8.61 

282 

8.61 

334 

8.61 

385 

8.61 

436 

8.61 487 

8.61 538 

37 


22 ' 

8.61 

589 

8.61 

640 

8.61 

691 

8.61 

742 

8.61 792 

8.61 843 

37 


23 ' 

8.61 

894 

8.61 

944 

8.61 

995 

8.62 

045 

8.62 096 

8.62 146 

38 


24 ' 

8.62 

196 

8.62 

246 

8.62 

297 

8.62 

347 

8.62 397 

8.62 447 

38 


25 ' 

8.62 

497 

8.62 

546 

8.62 

596 

8.62 

646 

8.62 696 

8.62 745 

39 


26 ' 

8.62 

795 

8.62 

844 

8.62 

894 

8.62 

943 

8.62 993 

8.63 042 

39 

^ gcq 

27 ' 

8.63 

091 

8.63 

140 

8.63 

189 

8.63 

238 

8.63 288 

8.63 336 

40 

1 ^ 1 

28 ' 

8.63 

385 

8.63 

434 

8.63 

483 

8.63 

532 

8.63 580 

8.63 629 

41 


29 ' 

8.63 

678 

8.63 

726 

8.63 

775 

8.63 

823 

8.63 871 

8.63 920 

41 


2° 30' 

8.63 

968 

8.64 

016 

8.64 

064 

8.64 

112 

8.64 160 

8.64 208 

42 


31 ' 

8.64 

256 

8.64 

304 

8.64 

352 

8.64 

400 

8.64 448 

8.64 495 

42 


32 ' 

8.64 

543 

8.64 

590 

8.64 

638 

8.64 

685 

8.64 733 

8.64 780 

43 

O 03 II 

33 ' 

8.64 

827 

8.64 

875 

8.64 

922 

8.64 

969 

8.65 016 

8.65 063 

43 


34 ' 

8.65 

no 

8.65 

157 

8.65 

204 

8.65 

251 

8.65 298 

8.65 344 

44 

M P DQ 
o 52 0 , 

35 ' 

8.65 

391 

8.65 

438 

8.65 

484 

8.65 

531 

8.65 577 

8.65 624 

44 


36 ' 

8.65 

670 

8.65 

717 

8.65 

763 

8.65 

809 

8.65 855 

8.65 901 

45 


37 ' 

8.65 

947 

8.65 

994 

8.66 

040 

8.66 

085 

8.66 131 

8.66 177 

46 

1 id ^ 

38 ' 

8.66 

223 

8.66 

269 

8.66 

314 

8.66 

360 

8.66 406 

8.66 451 

46 


39 ' 

8.66 

497 

8.66 

542 

8.66 

588 

8.66 

633 

8.66 678 

8.66 724 

47 

^ S ‘ 

2° 40' 

8.66 

769 

8.66 

814 

8.66 

859 

8.66 

904 

8.66 949 

8.66 994 

47 

PCt|0 

■S 2 

41 ' 

8.67 

039 

8.67 

084 

8.67 

129 

8.67 

174 

8.67 219 

8.67 263 

48 

” 05 

.•'P' 

42 ' 

8.67 

308 

8.67 

353 

8.67 

397 

8.67 

442 

8.67 486 

8.67 531 

48 

OOP 

43 ' 

8.67 

575 

8.67 

619 

8.67 

664 

8.67 

708 

8.67 752 

8.67 796 

49 

•“( cj +s 

44 ' 

8.67 

841 

8.67 

885 

8.67 

929 

8.67 

973 

8.68 017 

8.68 060 

49 

II 'ft II 

45 ' 

8.68 

104 

8.68 

148 

8.68 

192 

8.68 

236 

8.68 279 

8.68 323 

50 


46 ' 

8.68 

367 

8.68 

410 

8.68 

454 

8.68 

497 

8.68 540 

8.68 584 

51 


47 ' 

8.68 

627 

8.68 

670 

8.68 

714 

8.68 

757 

8.68 800 

8.68 843 

51 


48 ' 

8.68 

886 

8.68 

929 

8.68 

972 

8.69 

015 

8.69 058 

8.69 101 

52 

M+J 

O _ “ 

49 ' 

8.69 

144 

8.69 

187 

8.69 

229 

8.69 

272 

8.69 315 

8.69 357 

53 


2° 60' 

8.69 

400 

8.69 

442 

8.69 

485 

8.69 

527 

8.69 570 

8.69 612 

53 

I 

51 ' 

8.69 

654 

8.69 

697 

8.69 

739 

8.69 

781 

8.69 823 

8.69 865 

54 

go 

52 ' 

8.69 

907 

8.69 

949 

8.69 

991 

8.70 

033 

8.70 075 

8.70 117 

55 

iP 2s. 

53 ' 

8.70 

159 

8.70 

201 

8.70 

242 

8.70 

284 

8.70 326 

8.70 367 

55 


54 ' 

8.70 

409 

8.70 

451 

8.70 

492 

8.70 

534 

8.70 575 

8.70 616 

56 

■g (D « 

55 ' 

8.70 

658 

8.70 

699 

8.70 

740 

8.70 

781 

8.70 823 

8.70 864 

56 

II 

56 ' 

8.70 

905 

8.70 

946 

8.70 

987 

8.71 

028 

8.71 069 

8.71 no 

57 

(D 

57 ' 

8.71 

151 

8.71 

192 

8.71 

232 

8.71 

273 

8.71 314 

8.71 355 

58 

c^ap 

58 ' 

8.71 

395 

8.71 

436 

8.71 

476 

8.71 

517 

8.71 557 

8.71 598 

58 

c3 .2 

59 ' 

8.71 

638 

8.71 

679 

8.71 

719 

8.71 

759 

8.71 800 

8.71 840 

59 


































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


25 


0 ° 


/ 

L Sin 

L Xsin . 

L Cot 

L Cos 


Prop . Pts . 

0 





_ 

10.00 000 

60 


1 

6.46 

373 

6.46 

373 

13.53 627 

10.00 000 

59 


2 

6.76 

476 

6.76 

476 

13.23 524 

10.00 000 

58 


3 

6.94 

085 

6.94 

085 

13.05 915 

10.00 000 

57 


4 

7.06 

579 

7.06 

579 

12.93 421 

10.00 000 

56 


5 

7.16 

270 

7.16 

270 

12.83 730 

10.00 000 

55 


6 

7.24 

188 

7.24 

188 

12.75 812 

10.00 000 

54 


7 

7.30 

882 

7.30 

882 

12.69 118 

10.00 000 

53 


8 

7.36 

682 

7.36 

682 

12.63 318 

10.00 000 

52 


9 

7.41 

797 

7.41 

797 

12.58 203 

10.00 000 

51 


10 

7.46 

373 

7.46 

373 

12.53 627 

10.00 000 

50 


11 

7.50 

512 

7.50 

512 

12.49 488 

10.00 000 

49 


12 

7.54 

291 

7.54 

291 

12.45 709 

10.00 000 

48 


13 

7.57 

767 

7.57 

767 

12.42 233 

10.00 000 

47 


14 

7.60 

985 

7.60 

986 

12.39 014 

10.00 000 

46 


15 

7.63 

982 

7.63 

982 

12.36 018 

10.00 000 

45 


16 

7.66 

784 

7.66 

785 

12.33 215 

10.00 000 

44 


17 

7.69 

417 

7.69 

418 

12.30 582 

9.99 999 

43 

® 

18 

7.71 

900 

7.71 

900 

12.28 100 

9.99 999 

42 

bC . 
c3 ® 

19 

7.74 

248 

7.74 

248 

12.25 752 

9.99 999 

41 

ft 9 

20 

7.76 

475 

7.76 

476 

12.23 524 

9.99 999 

40 


21 

7.78 

594 

7.78 

595 

12.21 405 

9.99 999 

39 

o’C 

^ o3 

22 

7.80 

615 

7.80 

615 

12.19 385 

9.99 999 

38 

M 

23 

7.82 

545 

7.82 

546 

12.17 454 

9.99 999 

37 

OJ — 

24 

7.84 

393 

7.84 

394 

12.15 606 

9.99 999 

36 

“‘S 

25 

7.86 

166 

7.86 

167 

12.13 833 

9.99 999 

35 

. m 

26 

7.87 

870 

7.87 

871 

12.12 129 

9.99 999 

34 


27 

7.89 

509 . 

7.89 

510 

12.10 490 

9.99 999 

33 

f -, 

o ^ 

28 

7.91 

088 

7.91 

089 

12.08 911 

9.99 999 

32 

CTJ 

29 

7.92 

612 

7.92 

613 

12.07 387 

9.99 998 

31 


30 

7.94 

084 

7.94 

086 

12.05 914 

9.99 998 

30 


31 

7.95 

508 

7.95 

510 

12.04 490 

9.99 998 

29 

■^1 

32 

7.96 

887 

7.96 

889 

12.03 111 

9.99 998 

28 


33 

7.98 

223 

7.98 

225 

12.01 775 

9.99 998 

27 

(D g 

34 

7.99 

520 

7.99 

522 

12.00 478 

9.99 998 

26 


35 

8.00 

779 

8.00 

781 

11.99 219 

9.99 998 

25 

o o 

36 

8.02 

002 

8.02 

004 

11.97 996 

9.99 998 

24 


37 

8.03 

192 

8.03 

194 

11.96 806 

9.99 997 

23 

^ o 

38 

8.04 

350 

8.04 

353 

11.95 647 

9.99 997 

22 


39 

8.05 

478 

8.05 

481 

11.94 519 

9.99 997 

21 


40 

8.06 

578 

8.06 

581 

11.93 419 

9.99 997 

20 

.sS 

41 

8.07 

650 

8.07 

653 

11.92 347 

9.99 997 

19 

TO 

42 

8.08 

696 

8.08 

700 

11.91 300 

9.99 997 

18 


43 

8.09 

718 

8.09 

722 

11.90 278 

9.99 997 

17 


44 

8.10 

717 

8.10 

720 

11.89 280 

9.99 996 

16 

o 

45 

8.11 

693 

8.11 

696 

11.88 304 

9.99 996 

15 

h 

46 

8.12 

647 

8.12 

651 

11.87 349 

9.99 996 

14 


47 

8.13 

581 

8.13 

585 

11.86 415 

9.99 996 

13 


48 

8.14 

495 

8.14 

500 

11.85 500 

9.99 996 

12 


49 

8.15 

391 

8.15 

395 

11.84 605 

9.99 996 

11 


50 

8.16 

268 

8.16 

273 

11.83 727 

9.99 995 

10 


51 

8.17 

128 

8.17 

133 

11.82 867 

9.99 995 

9 


52 

8.17 

971 

8.17 

976 

11.82 024 

9.99 995 

8 


53 

8.18 

798 

8.18 

804 

11.81 196 

, 9.99 995 

7 


54 

8.19 

610 

8.19 

616 

11.80 384 

9.99 995 

6 


55 

8.20 

407 

8.20 

413 

11.79 587 

9.99 994 

5 


56 

8.21 

189 

8.21 

195 

11.78 805 

9.99 994 

4 


57 

8.21 

958 

8.21 

964 

11.78 036 

9.99 994 

3 


58 

8.22 

713 

8.22 

720 

11.77 280 

9.99 994 

2 


59 

8.23 

456 

8.23 

462 

11.76 538 

9.99 994 

1 


60 

8.24 

186 1 

8.24 

192 

11.75 808 

9.99 993 

0 



L Cos 

L Cot 

L Tan 

L Sin 

' 

Prop . Pts . 


89 





























26 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


1 ° 


' 

L Sin 

L Tan 

L Cot 

L Cos. 


Prop. Pts. 

0 

8.24 186 

8.24 192 

11.75 808 

9.99 993 

60 


1 

8.24 903 

8.24 910 

11.75 090 

9.99 993 

59 


2 

8.25 609 

8.25 616 

11.74 384 

9.99 993 

58 


3 

8.26 304 

8.26 312 

11.73 688 

9.99 993 

57 


4 

8.26 988 

8.26 996 

11.73 004 

9.99 992 

56 


5 

8.27 661 

8.27 669 

11.72 331 

9.99 992 

55 


6 

8.28 324 

8.28 332 

11.71 668 

9.99 992 

54 


7 

8.28 977 

8.28 986 

11.71 014 

9.99 992 

53 


8 

8.29 621 

8.29 629 

11.70 371 

9.99 992 

52 


9 

8.30 255 

8.30 263 

11.69 737 

9.99 991 

51 


10 

8.30 879 

8.30 888 

11.69 112 

9.99 991 

50 


11 

8.31 495 

8.31 505 

11.68 495 

9.99 991 

49 


12 

8.32 103 

8.32 112 

11.67 888 

9.99 990 

48 


13 

8.32 702 

8.32 711 

11.67 289 

9.99 990 

47 


14 

8.33 292 

8.33 302 

11.66 698 

9.99 990 

46 


15 

8.33 875 

8.33 886 

11.66 114 

9.99 990 

45 


16 

8.34 450 

8.34 461 

11.65 539 

9.99 989 

44 


17 

8.35 018 

8.35 029 

11.64 971 

9.99 989 

43 

O 

18 

8.35 578 

8.35 590 

11.64 410 

9.99 989 

42 


19 

8.36 131 

8.36 143 

11.63 857 

9.99 989 

41 

a 

^ . 

20 

8.36 678 

8.36 689 

11.63 311 

9.99 988 

40 

a 

21 

8.37 217 

8.37 229 

11.62 771 

9.99 988 

39 


22 

8.37 750 

8.37 762 

11.62 238 

9.99 988 

38 

® .■£ 

23 

8.38 276 

8.38 289 

11.61 711 

9.99 987 

37 

m 03 

24 

8.38 796 

8.38 809 

11.61 191 

9.99 987 

36 

M 

O 

25 

8.39 310 

8.39 323 

11.60 677 

9.99 987 

35 


26 

8.39 818 

8.39 832 

11.60 168 

9.99 986 

34 

> o 

27 

8.40 320 

8.40 334 

11.59 666 

9.99 986 

33 

t-i m 

o 2 

28 

8.40 816 

8.40 830 

11.59 170 

9.99 986 

32 


29 

8.41 307 

8.41 321 

11.58 679 

9.99 985 

31 


30 

8.41 792 

8.41 807 

11.58 193 

9.99 985 

30 


31 

8.42 272 

8.42 287 

11.57 713 

9.99 985 

29 

o3 

32 

8.42 746 

8.42 762 

11.57 238 

9.99 984 

28 


33 

8.43 216 

8.43 232 

11.56 768 

9.99 984 

27 


34 

8.43 680 

8.43 696 

11.56 304 

9.99 984 

26 


35 

8.44 139 

8.44 156 

11.55 844 

9.99 983 

25 

o S 

36 

8.44 594 

8.44 611 

11.55 389 

9.99 983 

24 

■3 ° 

37 

8.45 044 

8.45 061 

11.54 939 

9.99 983 

23 


38 

8.45 489 

8.45 507 

11.54 493 

9.99 982 

22 

'oO 

39 

8.45 930 

8.45 948 

11.54 052 

9.99 982 

21 

fcn ■ 

40 

8.46 366 

8.46 385 

11.53 615 

9.99 982 

20 

.as 

41 

8.46 799 

8.46 817 

11.53 183 

9.99 981 

19 

Ti 1-^ 

42 

8.47 226 

8.47 245 

11.52 755 

9.99 981 

18 

11 

43 

8.47 650 

8.47 669 

11.52 331 

9.99 981 

17 

I- 

44 

8.48 069 

8.48 089 

11.51 911 

9.99 980 

16 

w CO 

O ^ 

45 

8.48 485 

8.48 505 

11.51 495 

9.99 980 

15 


46 

8.48 896 

8.48 917 

11.51 083 

9.99 979 

14 


47 

8.49 304 

8.49 325 

11.50 675 

9.99 979 

13 


48 

8.49 708 

8.49 729 

11.50 271 

9.99 979 

12 


49 

8.50 108 

8.50 130 

11.49 870 

9.99 978 

11 


60 

8.50 504 

8.50 527 

11.49 473 

9.99 978 

10 


51 

8.50 897 

8.50 920 

11.49 080 

9.99 977 

9 


52 

8.51 287 

8.51 310 

11.48 690 

9.99 977 

8 


53 

8.51 673 

8.51 696 

11.48 304 

9.99 977 

7 


54 

8.52 055 

8.52 079 

11.47 921 

9.99 976 

6 


55 

8.52 434 

1 8.52 459 

11.47 541 

9.99 976 

5 


56 

8.52 810 

8.52 835 

11.47 165 

9.99 975 

4 


57 

8.53 183 

8.53 208 

11.46 792 

9.99 975 

3 


58 

8.53 552 

8.53 578 

11.46 422 

9.99 974 

2 


59 

8.53 919 

8.53 945 

11.46 055 

9.99 974 

1 


60 

8.54 282 

8.54 308 

11.45 692 

9.99 974 

0 



L Cos 

L Cot 

L Tan 

L Sin 

' 

Prop. Pts. 


88 ' 














































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


27 


2 ° 



L Sin 

L Tan 

L Cot 

L Cos 


Prop. Pts. 

0 

8.54 282 

8.54 308 

11.45 692 

9.99 974 

60 


1 

8.54 642 

8.54 669 

11.45 331 

9.99 973 

59 


2 

8.54 999 

8.55 027 

11.44 973 

9.99 973 

58 


3 

8.55 354 

8.55 382 

11.44 618 

9.99 972 

57 


4 

8.55 705 

8.55 734 

11.44 266 

9.99 972 

56 


5 

8.56 054 

8.56 083 

11.43 917 

9.99 971 

55 


6 

8.56 400 

8.56 429 

11.43 571 

9.99 971 

54 


7 

8.56 743 

8.56 773 

11.43 227 

9.99 970 

53 


8 

8.57 084 

8.57 114 

11.42 886 

9.99 970 

52 


9 

8.57 421 

8.57 452 

11.42 548 

9.99 969 

51 


10 

8.57 757 

8.57 788 

11.42 212 

9.99 969 

50 


11 

8.58 089 

8.58 121 

11.41 879 

9.99 968 

49 


12 

8.58 419 

8.58 451 

11.41 549 

9.99 968 

48 


13 

8.58 747 

8.58 779 

11.41 221 

9.99 967 

47 


14 

8.59 072 

8.59 105 

11.40 895 

9;99 967 

46 


15 

8.59 395 

8.59 428 

11.40 572 

9.99 967 

45 


16 

8.59 715 

8.59 749 

11.40.251 

9.99 966 

44 

IN 

17 

8.60 033 

8.60 068 

11.39 932 

9.99 966 

43 

Si. 

18 

8.60 349 

8.60 384 

11.39 616 

9.99 965 

42 


19 

8.60 662 

8.60 698 

11.39 302 

9.99 964 

41 

a 

II 

20 

8.60 973 

8.61 009 

11.38 991 

9.99 964 

40 

21 

8.61 282 

8.61 319 

11.38 681 

9.99 963 

39 

22 

8.61 589 

8.61 626 

11.38 374 

9.99 963 

38 

o 

23 

8.61 894 

8.61 931 

11.38 069 

9.99 962 

37 

24 

8.62 196 

8.62 234 

11.37 766 

9.99 962 

36 

25 

8.62 497 

8.62 535 

11.37 465 

9.99 961 

35 

j5<+h 

26 

8.62 795 

8.62 834 

11.37 166 

9.99 961 

34 

> ° 

27 

8.63 091 

8.63 131 

11.36 869 

9.99 960 

33 

o 1 

28 

8.63 385 

8.63 426 

11.36 574 

9.99 960 

32 


29 

8.63 678 

8.63 718 

11.36 282 

9.99 959 

31 

. ^ TO 

> > 

30 

8.63 968 

8.64 009 

11.35 991 

9.99 959 

30 


31 

8.64 256 

8.64 298 

11.35 702 

9.99 958 

29 

2 ^ 

32 

8.64 543 

8.64 585 

11.35 415 

9.99 958 

28 


33 

8.64-827 

8.64 870 

11.35 130 

9.99 957 

27 

4) .a 

d J 

34 

8.65 110 

8.65 154 

11.34 846 

9.99 956 

26 

35 

8.65 391 

8.65 435 

11.34 565 

9.99 956 

25 


36 

8.65 670 

8.65 715 

1 11.34 285 

j 9.99 955 

24 

.2 ® 

37 

8.65 947 

8.65 993 

1 11.34 007 

9.99 955 

23 

a 

38 

8.66 223 

8.66 269 

11.33 731 

9.99 954 

22 

39 

8.66 497 

8.66 543 

11.33 457 

9.99 954 

21 


40 

8.66 769 

8.66 816 

11.33 184 

9.99 953 

20 

"S s 

41 

8.67 039 

8.67 087 

11.32 913 

9.99 952 

19 


42 

8.67 308 

8.67 356 

11.32 644 

9.99 952 

18 

‘o ® 

43 

8.67 575 

8.67 624 

1 11.32 376 

9.99 951 

17 


44 

8.67 841 

8.67 890 

11.32 110 

9.99 951 

16 

d 

45 

8.68 104 

8.68 154 

11.31 846 

9.99 950 

15 

46 

8.68 367 

8.68 417 

11.31 583 

9.99 949 

14 


47 

8.68 627 

8.68 678 

11.31 322 

9.99 949 

13 


48 

8.68 886 

8.68 938 

11.31 062 

9.99 948 

12 


49 

8.69 144 

8.69 196 

11.30 804 

9.99 948 

11 


50 

8.69 400 

8.69 453 

11.30 547 

9.99 947 

10 


51 

8.69 654 

8.69 708 

11.30 292 

9.99 946 

9 


52 

8.69 907 

8.69 962 

11.30 038 

9.99 946 

8 


53 

8.70 159 

8.70 214 

11.29 786 

9.99 945 

7 


54 

8.70 409 

8.70 465 

11.29 535 

9.99 944 

6 


55 

8.70 658 

8.70 714 

11.29 286 

9.99 944 

5 


56 

8.70 905 

8.70 962 

11.29 038 

9.99 943 

4 


57 

8.71 151 

8.71 208 

11.28 792 

9.99 942 

3 


58 

8.71 395 

8.71 453 

11.28 547 

9.99 942 

2 


59 

8 71 638 

8.71 697 

11.28 303 

9.99 941 

1 


60 

8.71 880 

8.71 940 

11.28 060 

9.99 940 

0 



L Cos 

L Cot 

' L Tan 

1 L Sin 

' 

Prop. Pts. 


87 ' 
































































28 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


3 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 



0 

2 

3 

4 

8.71 880 

8.72 120 
8.72 359 
8.72.597 
8.72 834 

240 

239 

238 

237 

235 

234 

232 

232 

230 

229 

228 

226 

226 

224 

223 

222 

220 

220 

219 

217 

216 

216 

214 

213 

212 

211 

210 

209 

208 

208 

206 

205 

204 

203 

202 

201 

201 

199 

199 

197 

197 

196 

195 

194 

193 

192 

192 

190 

190 

189 

188 

187 

187 

186 

185 

184 

183 

183 

181 

181 

8.71 940 

8.72 181 
8.72 420 
8.72 659 
8.72 896 

241 

239 

239 

237 

236 

234 

234 

232 

231 

229 

229 

227 

226 

225 

224 

222 

222 

220 

219 

219 

217 

216 

215 

214 

213 

211 

211 

210 

209 

208 

206 

206 

205 

204 

203 

202 

201 

201 

199 

198 

198 

196 

196 

195 

194 

193 

192 

192 

190 

190 

189 

188 

188 

186 

186 

185 

184 

184 

182 

182 

11.28 060 
11.27 819 
11.27 580 
11.27 341 
11.27 104 

9.99 940 
9.99 940 
9.99 939 
9.99 938 
9.99 938 

60 

59 

58 

57 

56 


5 

6 

7 

8 

9 

8.73 069 
8.73 303 
8.73 535 
8.73 767 
8.73 997 

8.73 132 
8.73 366 
8.73 600 

8.73 832 

8.74 063 

11.26 868 
11.26 634 
11.26 400 
11.26 168 
11.25 937 

9.99 937 
9.99 936 
9.99 936 
9.99 935 
9.99 934 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

8.74 226 
8.74 454 
8.74 680 

8.74 906 

8.75 130 

8.74 292 
8.74 521 
8.74 748 

8.74 974 

8.75 199 

11.25 708 
11.25 479 
11.25 252 
11.25 026 
11.24 801 

9.99 934 
9.99 933 
9.99 932 
9.99 932 
9.99 931 

50 

49 

48 

47 

46 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 

8.75 353 
8.75 575 

8.75 795 

8.76 015 
8.76 234 

8.75 423 
8.75 645 

8.75 867 

8.76 087 
8.76 306 

11.24 577 
11.24 355 
11.24 133 
11.23 913 
11.23 694 

9.99 930 
9.99 929 
9.99 929 
9.99 928 
9.99 927 

45 

44 

43 

42 

41 

8.76 451 
8.76 667 

8.76 883 

8.77 097 
8.77 310 

8.76 525 
8.76 742 

8.76 958 

8.77 173 
8.77 387 

11.23 475 
11.23 258 
11.23 042 
11.22 827 
11.22 613 

9.99 926 
9.99 926 
9.99 925 
9.99 924 
9.99 923 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

8.77 522 
8.77 733 

8.77 943 

8.78 152 
8.78 360 

8.77 600 

8.77 811 

8.78 022 
8.78 232 
8.78 441 

11.22 400 
11.22 189 
11.21 978 
11.21 768 
11.21 559 

9.99 923 
9.99 922 
9.99 921 
9.99 920 
9.99 920 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

8.78 568 
8.78 774 

8.78 979 

8.79 183 
8.79 386 

8.78 649 

8.78 855 

8.79 061 
8.79 266 
8.79 470 

11.21 351 
11.21 145 
11.20 939 
11.20 734 
11.20 530 

9.99 919 
9.99 918 
9.99 917 
9.99 917 
9.99 916 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

8.79 588 
8.79 789 

8.79 990 

8.80 189 
8.80 388 

8.79 673 

8.79 875 

8.80 076 
8.80 277 
8.80 476 

11.20 327 
11.20 125 
11.19 924 
11.19 723 
11.19 524 

9.99 915 
9.99 914 
9.99 913 
9.99 913 
9.99 912 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

8.80 585 
8.80 782 

8.80 978 

8.81 173 
8.81 367 

8.80 674 

8.80 872 

8.81 068 
8.81 264 
8.81 459 

11.19 326 
11.19 128 
11.18 932 
11.18 736 
11.18 541 

9.99 911 
9.99 910 
9.99 909 
9.99 909 
9.99 908 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

45 

46 

47 

48 

49 

8.81 560 
8.81 752 

8.81 944 

8.82 134 
8.82 324 

8.81 653 

8.81 846 

8.82 038 
8.82 230 
8.82 420 

11.18 347 
11.18 154 
11.17 962 
11.17 770 
11.17 580 

9.99 907 
9.99 906 
9.99 905 
9.99 904 
9.99 904 

50 

51 

52 

53 

54 

8.82 513 

8.82 701 
8.82 888 

8.83 075 
8.83 261 

8.82 610 
8.82 799 

8.82 987 

8.83 175 
8.83 361 

11.17 390 
11.17 201 
11.17 013 
11.16 825 
11.16 639 

9.99 903 
9.99 902 
9.99 901 
9.99 900 
9.99 899 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

8.83 446 
8.83 630 
8.83 813 

8.83 996 

8.84 177 

8.83 547 
8.83 732 

8.83 916 

8.84 100 
8.84 282 

11.16 453 
11.16 268 
11.16 084 
11.15 900 
11.15 718 

9.99 898 
9.99 898 
9.99 897 
9.99 896 
9.99 895 

5 

4 

3 

2 

1 

60 

8.84 358 

8.84 464 

11.15 536 

9.99 894 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

' 



Prop. Pts. 


Prop. Pts. 


86 ' 


See opposite page for Proportional Parts. 








































































FIVE-PLACE LOGARITHMS OF FUNCTIONS 


29 


Proportional Parts for S'" 


» 

241 

240 

239 

238 

237 

236 

235 

234 

232 

231 

230 

6 

24.1 

24.0 

23.9 

23.8 

23.7 

23.6 

23.5 

23.4 

23.2 

23.1 

23.0 

7 

28.1 

28.0 

27.9 

27.8 

27.6 

27.5 

27.4 

27.3 

27.1 

27.0 

26.8 

8 

32.1 

32.0 

31.9 

31.7 

31.6 

31.5 

31.3 

31.2 

30.9 

30.8 

30.7 

9 

36.2 

36.0 

35.8 

35.7 

35.6 

35.4 

35.2 

35.1 

34.8 

34.7 

34.5 

10 

40.2 

40.0 

39.8 

39.7 

39.5 

39.3 

39.2 

39.0 

38.7 

38.5 

38.3 

20 

80.3 

80.0 

79.7 

79.3 

79.0 

78.7 

78.3 

78.0 

77.3 

77.0 

76.7 

30 

120.5 

120.0 

119.5 

119.0 

118.5 

118.0 

117.5 

117.0 

116.0 

115.5 

115.0 

40 

160.7 

160.0 

159.3 

158.7 

158.0 

157.3 

156.7 

156.0 

154.7 

154.0 

153.3 

50 

200.8 

200.0 

199.2 

198.3 

197.5 

196.7 

195.8 

195.0 

193.3 

192.5 

191.7 

// 

229 

228 

227 

226 

225 

224 

223 

222 

220 

219 

217 

6 

22.9 

22.8 

22.7 

22.6 

22.5 

22.4 

22.3 

22.2 

22.0 

21.9 

21.7 

7 

26.7 

26.6 

26.5 

26.4 

26.2 

26.1 

26.0 

25.9 

25.7 

25.6 

25.3 

8 

30.5 

30.4 

30.3 

30.1 

30.0 

29.9 

29.7 

29.6 

29.3 

29.2 

28.9 

9 

34.4 

34.2 

34.0 

33.9 

33.8 

33.6 

33.4 

33.3 

33.0 

32.9 

32.6 

10 

38.2 

38.0 

37.8 

37.7 

37.5 

37.3 

37.2 

37.0 

36.7 

36.5 

36.2 

20 

76.3 

76.0 

75.7 

75.3 

75.0 

74.7 

74.3 

74.0 

73.3 

73.0 

72.3 

30 

114.5 

114.0 

113.5 

113.0 

112.5 

112.0 

111.5 

111.0 

110.0 

109.5 

108.5 

40 

152.7 

152.0 

151.3 

150.7 

150.0 

149.3 

148.7 

148.0 

146.7 

146.0 

144.7 

50 

190.8 

190.0 

189.2 

188.3 

187.5 

186.7 

185.8 

185.0 

183.3 

182.5 

180.8 

» 

216 

215 

214 

213 

212 

211 

210 

209 

208 

206 

205 

6 

21.6 

21.5 

21.4 

21.3 

21.2 

21.1 

21.0 

20.9 

20.8 

20.6 

20.5 

7 

25.2 

25.1 

25.0 

24.9 

24.7 

24.6 

24.5 

24.4 

24.3 

24.0 

23.9 

8 

28.8 

28.7 

28.5 

28.4 

28.3 

28.1 

28.0 

27.9 

27.7 

27.5 

27.3 

9 

32.4 

32.2 

32.1 

32.0 

31.8 

31.6 

31.5 

31.4 

31.2 

30.9 

30.8 

10 

36.0 

35.8 

35.7 

35.5 

35.3 

35.2 

35.0 

34.8 

34.7 

34.3 

34.2 

20 

72.0 

71.7 

71.3 

71.0 

70.7 

70.3 

70.0 

69.7 

69.3 

68.7 

68.3 

30 

108.0 

107.5 

107.0 

106.5 

106.0 

105.5 

105.0 

104.5 

104.0 

103.0 

102.5 

40 

144.0 

143.3 

142.7 

142.0 

141.3 

140.7 

140.0 

139.3 

138.7 

137.3 

136.7 

50 

180.0 

179.2 

178.3 

177.5 

176.7 

175.8 

175.0 

174.2 

173.3 

171.7 

170.8 

" 

204 

203 

202 

201 

199 

198 

197 

196 

195 

194 

193 

6 

20.4 

20.3 

20.2 

20.1 

19.9 

19.8 

19.7 

19.6 

19.5 

19.4 

19.3 

7 

23.8 

23.7 

23.6 

23.4 

23.2 

23.1 

23.0 

22.9 

22.8 

22.6 

22.5 

8 

27.2 

27.1 

26.9 

26.8 

26.5 

26.4 

26.3 

26.1 

26.0 

25.9 

25.7 

9 

30.6 

30.4 

30.3 

30.2 

29.8 

29.7 

29.6 

29.4 

29.2 

29.1 

29.0 

10 

34.0 

33.8 

33.7 

33.5 

33.2 

33.0 

32.8 

32.7 

32.5 

32.3 

32.2 

20 

68.0 

67.7 

67.3 

67.0 

66.3 

66.0 

65.7 

65.3 

65.0 

64.7 

64.3 

30 

102.0 

101.5 

101.0 

100.5 

99.5 

99.0 

98.5 

98.0 

97.5 

97.0 

96.5 

40 

136.0 

135.3 

134.7 

134.0 

132.7 

132.0 

131.3 

130.7 

130.0 

129.3 

128.7 

50 

170.0 

169.2 

168.3 

167.5 

165.8 

165.0 

164.2 

163.3 

162.5 

161.7 

160.8 


192 

190 

189 

188 

187 

186 

185 

184 

183 

182 

181 

6 

19.2 

19.0 

18.9 

18.8 

18.7 

18.6 

18.5 

18.4 

18.3 

18.2 

18.1 

7 

22.4 

22.2 

22.1 

21.9 

21.8 

21.7 

21.6 

21.5 

21.4 

21.2 

21.1 

8 

25.6 

25.3 

25.2 

25.1 

24.9 

24.8 

24.7 

24.5 

24.4 

24.3 

24.1 

9 

28.8 

28.5 

28.4 

28.2 

28.1 

27.9 

27.8 

27.6 

27.4 

27.3 

27.2 

10 

32.0 

31.7 

31.5 

31.3 

31.2 

31.0 

30.8 

30.7 

30.5 

30.3 

30.2 

20 

64.0 

63.3 

63.0 

62.7 

62.3 

62.0 

61.7 

61.3 

61.0 

60.7 

60.3 

30 

96.0 

95.0 

94.5 

94.0 

93.5 

93.0 

92.5 

92.0 

91.5 

91.0 

90.5 

40 

128.0 

126.7 

126.0 

125.3 

124.7 

124.0 

123.3 

122.7 

122.0 

121.3 

120.7 

50 

160.0 

158.3 

157.5 

156.7 

155.8 

155.0 

154.2 

153.3 

152.5 

151.7 

150.8 


























































30 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


4 ° 



L Sin 


L Tan 

c d 

L Cot 

L Cos 



0 

1 

2 

3 

4 

8.84 358 
8.84 539 
8.84 718 

8.84 897 

8.85 075 

181 

179 

179 

178 

177 

177 

176 

175 

175 

173 

173 

173 

171 

171 

171 

169 

169 

169 

167 

168 

166 

166 

165 

164 

164 

163 

163 

162 

162 

160 

161 

159 

159 

159 

158 

157 

157 

156 

155 

155 

155 

154 

153 

153 

152 

152 

151 

151 

150 

150 

149 

149 

148 

147 

147 

147 

146 

146 

145 

145 

8.84 464 
8.84 646 

8.84 826 

8.85 006 
8.85 185 

182 

180 

180 

179 

178 

177 

177 

176 

176 

174 

174 

174 

172 

172 

171 

171 

170 

169 

169 

168 

167 

167 

166 

165 

165 

165 

163 

163 

163 

161 

162 

160 

160 

160 

159 

158 

158 

157 

157 

156 

155 

155 

155 

153 

154 

153 

152 

152 

151 

151 

150 

150 

149 

148 

149 

147 

147 

147 

146 

146 

11.15 536 
11.15 354 
11.15 174 
11.14 994 
11.14 815 

9.99 894 
9.99 893 
9.99 892 
9.99 891 
9.99 891 

60 

59 

58 

57 

56 


5 

6 

7 

8 

9 

8.85 252 
8.85 429 
8.85 605 
8.85 780 
8.85 955 

8.85 363 
8.85 540 
8.85 717 

8.85 893 

8.86 069 

11.14 637 
11.14 460 
11.14 283 
11.14 107 
11.13 931 

9.99 890 
9.99 889 
9.99 888 
9.99 887 
9.99 886 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

8.86 128 
8.86 301 
8.86 474 
8.86 645 
8.86 816 

8.86 243 
8.86 417 
8.86 591 
8.86 763 
8.86 935 

11.13 757 
11.13 583 
11.13 409 
11.13 237 
11.13 065 

9.99 885 
9.99 884 
9.99 883 
9.99 882 
9.99 881 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

8.86 987 

8.87 156 
8.87 325 
8.87 494 
8.87 661 

8.87 106 
8.87 277 
8.87 447 
8.87 616 
8.87 785 

11.12 894 
11.12 723 
11.12 553 
11.12 384 
11.12 215 

9.99 880 
9.99 879 
9.99 879 
9.99 878 
9.99 877 

45 

44 

43 

42 

41 

40 

39 

38 

37 

36 

20 

21 

22 

23 

24 

8.87 829 

8.87 995 

8.88 161 
8.88 326 
8.88 490 

8.87 953 

8.88 120 
8.88 287 
8.88 453 
8.88 618 

11.12 047 
11.11 880 
11.11 713 
11.11 547 
11.11 382 

9.99 876 
9.99 875 
9.99 874 
9.99 873 
9.99 872 

25 

26 

27 

28 
29 

8.88 654 
8.88 817 

8.88 980 

8.89 142 
8.89 304 

8.88 783 

8.88 948 

8.89 111 
8.89 274 
8.89 437 

11.11 217 
11.11 052 
11.10 889 
11.10 726 
11.10 563 

9.99 871 
9.99 870 
9.99 869 
9.99 868 
9.99 867 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

8.89 464 
8.89 625 
8.89 784 

8.89 943 

8.90 102 

8.89 598 
8.89 760 

8.89 920 

8.90 080 
8.90 240 

11.10 402 
11.10 240 
11.10 080 
11.09 920 
11.09 760 

9.99 866 
9.99 865 
9.99 864 
9.99 863 
9.99 862 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

8.90 260 
8.90 417 
8.90 574 
8.90 730 
8.90 885 

8.90 399 
8.90 557 
8.90 715 

8.90 872 

8.91 029 

11.09 601 
11.09 443 
11.09 285 
11.09 128 
11.08 971 

9.99 861 
9.99 860 
9.99 859 
9.99 858 
9.99 857 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

8.91 040 
8.91 195 
8.91 349 
8.91 502 
8.91 655 

8.91 185 
8.91 340 
8.91 495 
8.91 650 
8.91 803 

11.08 815 
11.08 660 
11.08 505 
11.08 350 
11.08 197 

9.99 856 
9.99 855 
9.99 854 
9.99 853 
9.99 852 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

8.91 807 

8.91 959 

8.92 110 
8.92 261 
8.92 411 

8.91 957 

8.92 110 
8.92 262 
8.92 414 
8.92 565 

11.08 043 
11.07 890 
11.07 738 
11.07 586 
11.07 435 

9.99 851 
9.99 850 
9.99 848 
9.99 847 
9.99 846 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

8.92 561 
8.92 710 

8.92 859 

8.93 007 
8.93 154 

8.92 716 

8.92 866 

8.93 016 
8.93 165 
8.93 313 

11.07 284 
11.07 134 
11.06 984 
11.06 835 
11.06 687 

9.99 845 
9.99 844 
9.99 843 
9.99 842 
9.99 841 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

8.93 301 
8.93 448 
8.93 594 
8.93 740 
8.93 885 

8.93 462 
8.93 609 
8.93 756 

8.93 903 

8.94 049 

11.06 538 
11.06 391 
11.06 244 
11.06 097 
11.05 951 

9.99 840 
9.99 839 
9.99 838 
9.99 837 
9.99 836 

5 

4 

3 

2 

1 

60 

8.94 030 

8.94 195 

11.05 805 

9.99 834 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

' 



Prop. Pts. 


Prop. Pts. 


86 ' 


See opposite page for Proportional Parts. 































































vr 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


Proportional Parts for 4“ 



182 

181 

180 

179 

178 

177 

176 

6 

18.2 

18.1 

18.0 

17.9 

17.8 

17.7 

17.6 

7 

21.2 

21.1 

21.0 

20.9 

20.8 

20.6 

20.5 

8 

24.3 

24.1 

24.0 

23.9 

23.7 

23.6 

23.5 

9 

27.3 

27.2 

27.0 

26.8 

26.7 

26.6 

26.4 

10 

30.3 

30.2 

30.0 

29.8 

29.7 

29.5 

29.3 

20 

60.7 

60.3 

6 J .0 

59.7 

59.3 

59.0 

58.7 

30 

91.0 

90.5 

90.0 

89.5 

89.0 

88.5 

88.0 

40 

121.3 

120.7 

120.0 

119.3 

118.7 

118.0 

117.3 

50 

151.7 

150.8 

150.0 

149.2 

148.3 

147.5 

146.7 

» 

175 

174 

173 

172 

171 

170 

169 

6 

17.5 

17.4 

17.3 

17.2 

17.1 

17.0 

16.9 

7 

20.4 

20.3 

20.2 

20.1 

20.0 

19.8 

19.7 

8 

23.3 

23.2 

23.1 

22.9 

22.8 

22.7 

22.5 

9 

26.2 

26.1 

26.0 

25.8 

25.6 

25.5 

25.4 

10 

29.2 

29.0 

28.8 

28.7 

28.5 

28.3 

28.2 

20 

58.3 

58.0 

57.7 

57.3 

57.0 

56.7 

56.3 

30 

87.5 

87.0 

86.5 

86.0 

85.5 

85.0 

84.5 

40 

116.7 

116.0 

115.3 

114.7 

114.0 

113.3 

112.7 

50 

145.8 

145.0 

144.2 

143.3 

142.5 

141.7 

140.8 

- 

168 

167 

166 

165 

164 

163 

162 

6 

16.8 

16.7 

16.6 

16.5 

16.4 

16.3 

16.2 

7 

19.6 

19.5 

19.4 

19.2 

19.1 

19.0 

18.9 

8 

22.4 

22.3 

22.1 

22.0 

21.9 

21.7 

21.6 

9 

25.2 

25.0 

24.9 

24.8 

24.6 

24.4 

24.3 

10 

28.0 

27.8 

27.7 

27.5 

27.3 

27.2 

27.0 

20 

56.0 

55.7 

55.3 

55.0 

54.7 

54.3 

54.0 

30 

84.0 

83.5 

83.0 

82.5 

82.0 

81.5 

81.0 

40 

112.0 

111.3 

110.7 

110.0 

109.3 

108.7 

108.0 

50 

140.0 

1 139.2 

138.3 

137.5 

136.7 

135.8 

135.0 


161 

160 

159 

158 

157 

156 

155 

6 

16.1 

16.0 

15.9 

15.8 

15.7 

15.6 

15.5 

7 

18.8 

18.7 

18.6 

18.4 

18.3 

18.2 

18.1 

8 

21.5 

21.3 

21.2 

21.1 

20.9 

20.8 

20.7 

9 

24.2 

24.0 

23.8 

23.7 

23.6 

23.4 

23.2 

10 

26.8 

26.7 

26.5 

26.3 

26.2 

26.0 

25.8 

20 

53.7 

53.3 

53.0 

52.7 

52.3 

52.0 

51.7 

30 

80.5 

80.0 

79.5 

79.0 

78.5 

78.0 

77.5 

40 

107.3 

106.7 

106.0 

105.3 

104.7 

104.0 

103.3 

50 

134.2 

133.3 

132.5 

131.7 

130.8 

130.0 

129.2 


154 

153 

152 

151 

150 

149 

148 

6 

15.4 

15.3 

15.2 

15.1 

15.0 

14.9 

14.8 

7 

18.0 

17.8 

17.7 

17.6 

17.5 

17.4 

17.3 

8 

20.5 

20.4 

20.3 

20.1 

20.0 

19.9 

19.7 

9 

23.1 

23.0 

22.8 

22.6 

22.5 

22.4 

22.2 

10 

25.7 

25.5 

25.3 

25.2 

25.0 

24.8 

24.7 

20 

51.3 

51.0 

50.7 

50.3 

50.0 

49.7 

49.3 

30 

77.0 

76.5 

76.0 

75.5 

75.0 

74.5 

74.0 

40 

102.7 

102.0 

101.3 

100.7 

100.0 

99.3 

98.7 

50 

128.3 

127.5 

126.7 

125.8 

125.0 

124.2 

123.3 


31 


For 147, 146, and 145 see page 32. 






































32 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


5 ° 


' 

L Sin 

d 

L T3,ii 

c d 

L Cot 

L Cos 


Prop. Pts. 

0 

1 

2 

3 

4 

8.94 030 
8.94 174 
8.94 317 
8.94 461 
8.94 603 

144 

143 

144 

142 

143 

141 

142 
141 
140 
140 

139 

139 

139 

138 

138 

137 

137 

136 

136 

136 

135 

135 

134 

134 

133 

133 

133 

132 

132 

131 

131 

131 

130 

130 

129 

129 

129 

128 

128 

128 

127 

127 

126 

126 

126 

125 

125 

124 

125 

123 

124 
123 
123 
122 
122 

122 

121 

121 

121 

120 

8.94 195 
8.94 340 
8.94 485 
8.94 630 
8.94 773 

145 

145 

145 

143 

144 

143 

142 

142 

142 

141 

140 

141 

139 

140 

138 

139 
138 

137 

138 

136 

137 

135 

136 
135 
135 

134 

134 

133 

133 

133 

132 

132 

131 

131 

131 

130 

130 

130 

129 

128 

129 

128 

127 

128 
127 

126 

126 

126 

126 

125 

125 

124 

124 

124 

123 

123 

123 

122 

122 

122 

11.05 805 
11.05 660 
11.05 515 
11.05 370 
11.05 227 

9.99 834 
9.99 833 
9.99 832 
9.99 831 
9.99 830 

60 

59 

58 

57 

56 

// 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

// 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

6 

7 

8 

9 

10 

20 

30 

40 

50 

147 

14.7 

17.2 

19.6 
22.0 

24.5 
49.0 

73.5 
98.0 

122.5 

143 

14.3 

16.7 

19.1 

21.4 

23.8 

47.7 

71.5 
95.3 

119.2 

139 

13.9 

16.2 

18.5 

20.9 

23.2 

46.3 

69.5 

92.7 

115.8 

135 

13.5 

15.8 
18.0 
20.2 

22.5 
45.0 

67.5 
90.0 

112.5 

131 

13.1 

15.3 

17.5 

19.6 

21.8 

43.7 

65.5 

87.3 

109.2 

127 

12.7 

14.8 

16.9 
19.0 

21.2 

42.3 

63.5 
84.7 

105.8 

123 

12.3 

14.4 

16.4 

18.4 

20.5 
41.0 

61.5 
82.0 

102.5 

146 

14.6 
17.0 

19.5 

21.9 

24.3 

48.7 
73.0 

97.3 

121.7 

142 

14.2 

16.6 

18.9 

21.3 

23.7 

47.3 
71.0 

94.7 

118.3 

138 

13.8 
16.1 

18.4 
20.7 
23.0 
46.0 
69.0 
92.0 

115.0 

134 

13.4 

15.6 

17.9 
20.1 

22.3 

44.7 
67.0 

89.3 

111.7 

130 

13.0 

15.2 

17.3 

19.5 

21.7 

43.3 
65.0 

86.7 

108.3 

126 

12.6 

14.7 

16.8 

18.9 
21.0 
42.0 
63.0 
84.0 

105.0 

122 

12.2 

14.2 

16.3 

18.3 

20.3 
40.7 
61.0 

81.3 

101.7 

145 

14.5 

16.9 
19.3 
21.8 

24.2 

48.3 

72.5 

96.7 
120.8 

141 

14.1 

16.4 

18.8 

21.2 

23.5 
47.0 

70.5 
94.0 

117.5 

137 

13.7 
16.0 

18.3 

20.6 

22.8 

45.7 

68.5 

91.3 

114.2 

133 

13.3 

15.5 

17.7 
20.0 
22.2 

44.3 

66.5 

88.7 
110.8 

129 

12.9 
15.0 

17.2 

19.4 

21.5 
43.0 

64.5 
86.0 

107.5 

125 

12.5 

14.6 

16.7 

18.8 

20.8 

41.7 

62.5 

83.3 

104.2 

121 

12.1 

14.1 

16.1 
18.2 
20.2 

40.3 

60.5 

80.7 
100.8 

144 

14.4 

16.8 

19.2 
21.6 
24.0 
48.0 
72.0 
96.0 

120.0 

140 

14.0 

16.3 

18.7 
21.0 

23.3 

46.7 
70.0 

93.3 
116.7 

136 

13.6 

15.9 
18.1 

20.4 

22.7 

45.3 
68.0 

90.7 

113.3 

132 

13.2 

15.4 

17.6 

19.8 
22.0 
44.0 
66.0 
88.0 

110.0 

128 

12.8 

14.9 

17.1 

19.2 

21.3 

42.7 
64.0 

85.3 
106.7 

124 

12.4 

14.5 

16.5 

18.6 

20.7 
41.3 
62.0 

82.7 

103.3 

120 

12.0 

14.0 

16.0 

18.0 

20.0 

40.0 

60.0 

80.0 

100.0 

5 

6 

7 

8 

9 

8.94 746 

8.94 887 

8.95 029 
8.95 170 
8.95 310 

8.94 917 

8.95 060 
8.95 202 
8.95 344 
8.95 486 

11.05 083 
11.04 940 
11.04 798 
11.04 656 
11.04 514 

9.99 829 
9.99 828 
9.99 827 
9.99 825 
9.99 824 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

8.95 450 
8.95 589 
8.95 728 

8.95 867 

8.96 005 

8.95 627 
8.95 767 

8.95 908 

8.96 047 
8.96 187 

11.04 373 
11.04 233 
11.04 092 
11.03 953 
11.03 813 

9.99 823 
9.99 822 
9.99 821 
9.99 820 
9.99 819 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

8.96 143 
8.96 280 
8.96 417 
8.96 553 
8.96 689 

8.96 325 
8.96 464 
8.96 602 
8.96 739 
8.96 877 

11.03 675 
11.03 536 
11.03 398 
11.03 261 
11.03 123 

9.99 817 
9.99 816 
9.99 815 
9.99 814 
9.99 813 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

8.96 825 

8.96 960 

8.97 095 
8.97 229 
8.97 363 

8.97 013 
8.97 150 
8.97 285 
8.97 421 
8.97 556 

11.02 987 
11.02 850 
11.02 715 
11.02 579 
11.02 444 

9.99 812 
9.99 810 
9.99 809 
9.99 808 
9.99 807 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

8.97 496 
8.97 629 
8.97 762 

8.97 894 

8.98 026 

8.97 691 
8.97 825 

8.97 959 

8.98 092 
8.98 225 

11.02 309 
11.02 175 
11.02 041 
11.01 908 
11.01 775 

9.99 806 
9.99 804 
9.99 803 
9.99 802 
9.99 801 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

8.98 157 
8.98 288 
8.98 419 
8.98 549 
8.98 679 

8.98 358 
8.98 490 
8.98 622 
8.98 753 
8.98 884 

11.01 642 
11.01 510 
11.01 378 
11.01 247 
11.01 116 

9.99 800 
9.99 798 
9.99 797 
9.99 796 
9.99 795 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

8.98 808 

8.98 937 

8.99 066 
8.99 194 
8.99 322 

8.99 015 
8.99 145 
8.99 275 
8.99 405 
8.99 534 

11.00 985 
11.00 855 
11.00 725 
11.00 595 
11.00 466 

9.99 793 
9.99 792 
9.99 791 
9.99 790 
9.99 788 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

8.99 450 
8.99 577 
8.99 704 
8.99 830 
8.99 956 

8.99 662 
8.99 791 
8.99 919 
9.0O046 
9.00 174 

11.00 338 
11.00 209 
11.00 081 
10.99 954 
10.99 826 

9.99 787 
9.99 786 
9.99 785 
9.99 783 
9.99 782 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.00 082 
9.00 207 
9.00 332 
9.00 456 
9.00 581 

9.00 301 
9.00 427 
9.00 553 
9.00 679 
9.00 805 

10.99 699 
10.99 573 
10.99 447 
10.99 321 
10.99 195 

9.99 781 
9.99 780 
9.99 778 
9.99 777 
9.99 776 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.00 704 
9.00 828 
9.00 951 
9.01 074 
9.01 196 

9.00 930 
9.01 055 
9.01 179 
9.01 303 
9.01 427 

10.99 070 
10.98 945 
10.98 821 
10.98 697 
10.98 573 

9.99 775 
9.99 773 
9.99 772 
9.99 771 
9.99 769 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.01 318 
9.01 440 
9.01 561 
9.01 682 
9.01 803 

9.01 550 
9.01 673 
9.01 796 
9.01 918 
9.02 040 

10.98 450 
10.98 327 
10.98 204 
10.98 082 
10.97 960 

9.99 768 
9.99 767 
9.99 765 
9.99 764 
9.99 763 

5 

4 

3 

2 

1 

60 

9.01 923 

9.02 162 

10.97 838 

9.99 761 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

/ 

Prop. Pts. 


84 ‘ 























































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


33 


6 ° 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 


0 

9.01 923 


9.02 162 


10.97 838 

9.99 761 

60 

1 

9.02 043 

120 

9.02 283 

121 

10.97 717 

9.99 760 

59 

2 

9.02 163 

120 

9.02 404 

121 

10.97 596 

9.99 759 

58 

3 

9.02 283 

120 

9.02 525 

121 

10.97 475 

9.99 757 

57 

4 

9.02 402 

119 

118 

9.02 645 

120 

121 

10.97 355 

9.99 756 

56 

5 

9.02 520 

9.02 766 

10.97 234 

9.99 755 

55 

6 

9.02 639 

119 

9.02 885 

119 

10.97 115 

9.99 753 

54 

7 

9.02 757 

118 

9.03 005 

120 

10.96 995 

9.99 752 

53 

8 

9.02 874 

117 

9.03 124 

119 

10.96 876 

9.99 751 

52 

9 

9.02 992 

118 

117 

9.03 242 

118 

119 

10.96 758 

9.99 749 

51 

10 

9.03 109 

9.03 361 

10.96 639 

9.99 748 

50 

11 

9.03 226 

117 

9.03 479 

118 

10.96 521 

9.99 747 

49 

12 

9.03 342 

116 

9.03 597 

118 

10.96 403 

9.99 745 

48 

13 

9.03 458 

116 

9.03 714 

117 

10.96 286 

9.99 744 

47 

14 

9.03 574 

116 

116 

9.03 832 

118 

116 

10.96 168 

9.99 742 

46 

15 

9.03 690 

9.03 948 

10.96 052 

9.99 741 

45 

16 

9.03 805 

115 

9.04 065 

117 

10.95 935 

9.99 740 

44 

17 

9.03 920 

115 

9.04 181 

116 

10.95 819 

9.99 738 

43 

18 

9.04 034 

114 

9.04 297 

116 

10.95 703 

9.99 737 

42 

19 

9.04 149 

115 
113 

9.04 413 

116 

11 

10.95 587 

9.99 736 

41 

20 

9.04 262 

9.04 528 

J. lO 

10.95 472 

9.99 734 

40 

21 

9.04 376 

114 

9.04 643 

115 

10.95 357 

9.99 733 

39 

22 

9.04 490 

114 

9.04 758 

115 

10.95 242 

9.99 731 

38 

23 

9.04 603 

113 

9.04 873 

115 

10.95 127 

9.99 730 

37 

24 

9.04 715 

112 

113 

9.04 987 

114 

114 

10.95 013 

9.99 728 

36 

25 

9.04 828 

9.05 101 

10.94 899 

9.99 727 

35 

26 

9.04 940 

112 

9.05 214 

113 

10.94 786 

9.99 726 

34 

27 

9.05 052 

112 

9.05 328 

114 

10.94 672 

9.99 724 

33 

28 

9.05 164 

112 

9.05 441 

113 

10.94 559 

9.99 723 

32 

29 

9.05 275 

111 

111 

9.05 553 

112 

113 

10.94 447 

9.99 721 

31 

30 

9.05 386 

9.05 666 

10.94 334 

9.99 720 

30 

31 

9.05 497 

111 

9.05 778 

112 

10.94 222 

9.99 718 

29 

32 

9.05 607 

110 

9.05 890 

112 

10.94 110 

9.99 717 

28 

33 

9.05 717 

110 

9.06 002 

112 

10.93 998 

9.99 716 

27 

34 

9.05 827 

110 

1 1 

9.06 113 

111 

111 

10.93 887 

9.99 714 

26 

35 

9.05 937 

i iU 

9.06 224 

111 

10.93 776 

9.99 713 

25 

36 

9.06 046 

109 

9.06 335 

111 

10.93 665 

9.99 711 

24 

37 

9.06 155 

109 

9.06 445 

110 

10.93 555 

9.99 710 

23 

38 

9.06 264 

109 

9.06 556 

111 

10.93 444 

9.99 708 

22 

39 

9.06 372 

108 

1 HQ 

9.06 666 

110 

109 

10.93 334 

9.99 707 

21 

40 

9.06 481 

luy 

9.06 775 


10.93 225 

9.99 705 

20 

41 

9.06 589 

108 

9.06 885 

110 

10.93 115 

9.99 704 

19 

42 

9.06 696 

107 

9.06 994 

109 

10.93 006 

9.99 702 

18 

43 

9.06 804 

108 

9.07 103 

109 

10.92 897 

9.99 701 

17 

44 

9.06 911 

107 

9.07 211 

108 

109 

10.92 789 

9.99 699 

16 

45 

9.07 018 

107 

9.07 320 

10.92 680 

9.99 698 

15 

46 

9.07 124 

106 

9.07 428 

108 

10.92 572 

9.99 696 

14 

47 

9.07 231 

107 

9.07 536 

108 

10.92 464 

9.99 695 

13 

48 

9.07 337 

106 

9.07 643 

107 

10.92 357 

9.99 693 

12 

49 

9.07 442 

105 

9.07 751 

108 

107 

10.92 249 

9.99 692 

11 

50 

9.07 548 

106 

9.07 858 

10.92 142 

9.99 690 

10 

51 

9.07 653 

105 

9.07 964 

106 

10.92 036 

9.99 689 

9 

52 

9.07 758 

105 

9.08 071 

107 

10.91 929 

9.99 687 

8 

53 

9.07 863 

105 

9.08 177 

106 

10.91 823 

9.99 686 

7 

54 

9.07 968 

105 

1 (\A 

9.08 283 

106 

1 HA 

10.91 717 

9.99 684 

6 

55 

9.08 072 

1U4 

9.08 389 

1 uu 

10.91 611 

9.99 683 

5 

56 

9.08 176 

104 

9.08 495 

106 

10.91 505 

9.99 681 

4 

57 

9.08 280 

104 

9.08 600 

105 

10.91 400 

9.99 680 

3 

58 

9.08 383 

103 

9.08 705 

105 

10.91 295 

9.99 678 

2 

59 

9.08 486 

103 

9.08 810 

105 

104 

10.91 190 

9.99 677 

1 

60 

9.08 589 

103 

9.08 914 

10.91 086 

9.99 675 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

/ 


Prop. Pts. 


" 

121 

120 

119 

6 

12.1 

12.0 

11.9 

7 

14.1 

14.0 

13.9 

8 

16.1 

16.0 

15.9 

9 

18.2 

18.0 

17.8 

10 

20.2 

20.0 

19.8 

20 

40.3 

40.0 

39.7 

30 

60.5 

60.0 

59.5 

40 

80.7 

80.0 

79.3 

50 

100.8 

100.0 

99.2 


118 

117 

116 

6 

11.8 

11.7 

11.6 

7 

13.8 

13.6 

13.5 

8 

15.7 

15.6 

15.5 

9 

17.7 

17.6 

17.4 

10 

19.7 

19.5 

19.3 

20 

39.3 

39.0 

38.7 

30 

59.0 

58.5 

58.0 

40 

78.7 

78.0 

77.3 

50 

98.3 

97.5 

96.7 

n 

115 

114 

113 

6 

11.5 

11.4 

11.3 

7 

13.4 

13.3 

13.2 

8 

15.3 

15.2 

15.1 

9 

17.2 

17.1 

17.0 

10 

19.2 

19.0 

18.8 

20 

38.3 

38.0 

37.7 

30 

57.5 

57.0 

56.5 

40 

76.7 

76.0 

75.3 

50 

95.8 

95.0 

94.2 

» 

112 

111 

110 

6 

11.2 

11.1 

11.0 

7 

13.1 

13.0 

12.8 

8 

14.9 

14.8 

14.7 

9 

16.8 

16.6 

16.5 

10 

18.7 

18.5 

18.3 

20 

37.3 

37.0 

36.7 

30 

56.0 

55.5 

55.0 

40 

74.7 

74.0 

73.3 

50 

93.3 

92.5 

91.7 

- 

109 

108 

107 

6 

10.9 

10.8 

10.7 

7 

12.7 

12.6 

12.5 

8 

14.5 

14.4 

14.3 

9 

16.4 

16.2 

16.0 

10 

18.2 

18.0 

17.8 

20 

36.3 

36.0 

35.7 

30 

54.5 

54.0 

53.5 

40 

72.7 

72.0 

71.3 

50 

90.8 

90.0 

89.2 


106 

105 

104 

6 

10.6 

10.5 

10.4 

7 

12.4 

12.2 

12.1 

8 

14.1 

14.0 

13.9 

9 

15.9 

15.8 

15.6 

10 

17.7 

17.5 

17.3 

20 

35.3 

35.0 

1 34.7 

30 

53.0 

• 52.5 

52.0 

40 

70.7 

70.0 

1 69.3 

50 

88.3 

. 87.5 

• 86.7 


Prop. Pts. 


83 ‘ 

















































































34 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 


0 

9.08 589 


9.08 914 


10.91 086 

9.99 675 

60 

1 

9.08 692 

103 

9.09 019 

105 

10.90 981 

9.99 674 

59 

2 

9.08 795 

103 

9.09 123 

104 

10.90 877 

9.99 672 

58 

3 

9.08 897 

102 

9.09 227 

104 

10.90 773 

9.99 670 

57 

4 

9.08 999 

102 

9.09 330 

103 

104 

10.90 670 

9.99 669 

56 

5 

9.09 101 


9.09 434 

10.90 566 

9.99 667 

55 

6 

9.09 202 

101 

9.09 537 

103 

10.90 463 

9.99 666 

54 

7 

9.09 304 

102 

9.09 640 

103 

10.90 360 

9.99 664 

53 

8 

9.09 405 

101 

9.09 742 

102 

10.90 258 

9.99 663 

52 

9 

9.09 506 

101 

100 

9.09 845 

103 

1 no 

10.90 155 

9.99 661 

51 

10 

9.09 606 

9.09 947 

lUZ 

10.90 053 

9.99 659 

50 

11 

9.09 707 

101 

9.10 049 

102 

10.89 951 

9.99 658 

49 

12 

9.09 807 

100 

9.10 150* 

101 

10.89 850 

9.99 656 

48 

13 

9.09 907 

100 

9.10 252 

102 

10.89 748 

9.99 655 

47 

14 

9.10 006 

99 

100 

9.10 353 

101 

10.89 647 

9.99 653 

46 

15 

9.10 106 

9.10 454 

lUl 

10.89 546 

9.99 651 

45 

16 

9.10 205 

99 

9.10 555 

101 

10.89 445 

9.99 650 

44 

17 

9.10 304 

99 

9.10 656 

101 

10.89 344 

9.99 648 

43 

18 

9.10 402 

98 

9.10 756 

100 

10.89 244 

9.99 647 

42 

19 

9.10 501 

99 

9.10 856 

100 

100 

10.89 144 

9.99 645 

41 

20 

9.10 599 


9.10 956 

10.89 044 

9.99 643 

40 

21 

9.10 697 

98 

9.11 056 

100 

10.88 944 

9.99 642 

39 

22 

9.10 795 

98 

9.11 155 

99 

10.88 845 

9.99 640 

38 

23 

9.10 893 

98 

9.11 254 

99 

10.88 746 

9.99 638 

37 

24 

9.10 990 

97 

97 

9.11 353 

99 

QQ 

10.88 647 

9.99 637 

36 

25 

9.11 087 

9.11 452 

yy 

10.88 548 

9.99 635 

35 

26 

9.11 184 

97 

9.11 551 

99 

10.88 449 

9.99 633 

34 

27 

9.11 281 

97 

9.11 649 

98 

10.88 351 

9.99 632 

33 

28 

9.11 377 

96 

9.11 747 

98 

10.88 253 

9.99 630 

32 

29 

9.11 474 

97 

QA 

9.11 845 

98 

QC 

10.88 155 

9.99 629 

31 

30 

9.11 570 

yo 

9.11 943 

yo 

10.88 057 

9.99 627 

30 

31 

9.11 666 

96 

9.12 040 

97 

10.87 960 

9.99 625 

29 

32 

9.11 761 

95 

9.12 138 

98 

10.87 862 

9.99 624 

28 

33 

9.11 857 

96 

9.12 235 

97 

10.87 765 

9.99 622 

27 

34 

9.11 952 

95 

95 

9.12 332 

97 

Qfi 

10.87 668 

9.99 620 

26 

35 

9.12 047 

9.12 428 

yo 

10.87 572 

9.99 618 

25 

36 

9.12 142 

95 

9.12 525 

97 

10.87 475 

9.99 617 

24 

37 

9.12 236 

94 

9.12 621 

96 

10.87 379 

9.99 615 

23 

38 

9.12 331 

95 

9.12 717 

96 

10.87 283 

9.99 613 

22 

39 

9.12 425 

94 

94 

9.12 813 

96 

Q A 

10.87 187 

9.99 612 

21 

40 

9.12 519 

9.12 909 

y 0 

10.87 091 

9.99 610 

20 

41 

9.12 612 

93 

9.13 004 

95 

10.86 996 

9.99 608 

19 

42 

9.12 706 

94 

9.13 099 

95 

10.86 901 

9.99 607 

18 

43 

9.12 799 

93 

9.13 194 

95 

10.86 806 

9.99 605 

17 

44 

9.12 892 

93 

93 

9.13 289 

95 

95 

10.86 711 

9.99 603 

16 

45 

9.12 985 

9.13 384 

10.86 616 

9.99 601 

15 

46 

9.13 078 

93 

9.13 478 

94 

10.86 522 

9.99 600 

14 

47 

9.13 171 

93 

9.13 573 

95 

10.86 427 

9.99 598 

13 

48 

9.13 263 

92 

9.13 667 

94 

10.86 333 

9.99 596 

12 

49 

9.13 355 

92 

92 

9.13 761 

94 

93 

10.86 239 

9.99 595 

11 

60 

9.13 447 

9.13 854 

10.86 146 

9.99 593 

10 

51 

9.13 539 

92 

9.13 948 

94 

10.86 052 

9.99 591 

9 

52 

9.13 630 

91 

9.14 041 

93 

10.85 959 

9.99 589 

8 

53 

9.13 722 

92 

9.14 134 

93 

10.85 866 

9.99 588 

7 

54 

9.13 813 

91 

91 

9.14 227 

93 

93 

10.85 773 

9.99 586 

6 

55 

9.13 904 

9.14 320 

10.85 680 

9.99 584 

5 

56 

9.13 994 

90 

9.14 412 

92 

10.85 588 

9.99 582 

4 

57 

9.14 085 

91 

9.14 504 

92 

10.85 496 

9.99 581 

3 

58 

9.14 175 

90 

9.14 597 

93 

10.85 403 

9.99 579 

2 

59 

9.14 266 

91 

90 

9.14 688 

91 

92 

10.85 312 

9.99 577 

1 

60 

9.14 356 

9.14 780 

10.85 220 

9.99 575 

0 


L Cos ’ 

d 

L Cot 

c d 

L Tan 

L Sin 

i 


Prop. Pts. 


105 

104 

10.5 

10.4 

12.3 

12.1 

14.0 

13.9 

15.8 

15.6 

17.5 

17.3 

35.0 

34.7 

52.5 

52.0 

70.0 

69.3 

87.5 

86.7 

102 

101 

10.2 

10.1 

11.9 

11.8 

13.6 

13.5 

15.3 

15.2 

17.0 

16.8 

34.0 

33.7 

51.0 

50.5 

68.0 

67.3 

85.0 

84.2 


10.3 
12.0 

13.7 

15.4 

17.2 

34.3 

51.5 

68.7 

85.8 


100 

10.0 

11.7 

13.3 
15.0 

16.7 

33.3 
50.0 

66.7 

83.3 



99 

98 

97 

6 

9.9 

9.8 

9.7 

7 

11.6 

11.4 

11.3 

8 

13.2 

13.1 

12.9 

9 

14.8 

14.7 

14.6 

10 

16.5 

16.3 

16.2 

20 

33.0 

32.7 

32.3 

30 

49.5 

49.0 

48.5 

40 

66.0 

65.3 

64.7 

50 

82.5 

81.7 

80.8 

» 

96 

95 

94 

6 

9.6 

9.5 

9.4 

7 

11.2 

11.1 

11.0 

8 

12.8 

12.7 

12.5 

9 

14.4 

14.2 

14.1 

10 

16.0 

15.8 

15.7 

20 

32.0 

31.7 

31.3 

30 

48.0 

47.5 

47.0 

40 

64.0 

63.3 

62.7 

50 

80.0 

79.2 

78.3 


93 

92 

91 

6 

9.3 

9.2 

9.1 

7 

10.9 

10.7 

10.6 

8 

12.4 

12.3 

12.1 

9 

14.0 

13.8 

13.6 

10 

15.5 

15.3 

15.2 

20 

31.0 

30.7 

30.3 

30 

46.5 

46.0 

45.5 

40 

62.0 

61.3 

60.7 

50 

77.5 

76.7 

75.8 

» 

90 

2 

1 

6 

9.0 

0.2 

0.1 

7 

10.5 

0.2 

0.1 

8 

12.0 

0.3 

0.1 

9 

13.5 

0.3 

0.2 

10 

15.0 

0.3 

0.2 

20 

30.0 

0.7 

0.3 

30 

45.0 

1.0 

0.5 

40 

60.0 

1.3 

0.7 

50 

75.0 

1.7 

0.8 


Prop. Pts. 


82 ' 
















































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


35 


8 ° 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 


Prop. Pts. 

0 

9.14 356 


9.14 780 


10.85 220 

9.99 575 

60 





1 

9.14 445 


9.14 872 

92 

10.85 128 

9.99 574 

59 





2 

9.14 535 

90 

9.14 963 

91 

10.85 037 

9.99 572 

58 





3 

9.14 624 


9.15 054 

91 

10.84 946 

9.99 570 

57 

n 

92 

91 

90 

4 

9.14 714 

90 

89 

9.15 145 

91 

10.84 855 

9.99 568 

56 

6 

9 1 

j 9 ] 

1 9 0 

5 

9.14 803 

88 

9.15 236 


10.84 764 

9.99 566 

55 

7 

10.; 

r io;( 

5 10.5 

6 

9.14 891 

9.15 327 

91 

10.84 673 

9.99 565 

54 

8 

12.C 

5 12.] 

L 12.0 

7 

9.14 980 

89 

9.15 417 

90 

10.84 583 

9.99 563 

53 

9 

13.6 

5 13.f 

) 13.5 

8 

9.15 069 

89 

9.15 508 

91 

10.84 492 

9.99 561 

52 

10 

20 

15.5 
30 7 

! 15.5 
' 30 ^ 

! 15.0 
! 'in n 

9 

9.15 157 


9.15 598 

90 

90 

10.84 402 

9.99 559 

51 

30 

46.( 

) 45^5 

i oU.U 

; 45.0 

10 

9.15 245 


9.15 688 

10.84 312 

9.99 557 

50 

40 

61.3 

1 60.7 

60.0 

11 

9.15 333 

88 

9.15 777 

89 

10.84 223 

9.99 556 

49 

50 

76.7 

’ 75.8 

! 75.0 

12 

9.15 421 

88 

9.15 867 

90 

10.84 133 

9.99 554 

48 





13 

9.15 508 

87 

9.15 956 

89 

10.84 044 

9.99 552 

47 





14 

9.15 596 

88 

87 

9.16 046 

90 

10.83 954 

9.99 550 

46 



88 


15 

9.15 683 

9.16 135 


10.83 865 

9.99 548 

45 


o9 

87 

16 

9.15 770 

87 

9.16 224 

89 

10.83 776 

9.99 546 

44 

6 

8.9 

8.8 

8.7 

17 

9.15 857 


9.16 312 

88 

10.83 688 

9.99 545 

43 

7 

10.4 

10.3 

10.2 

18 

9.15 944 

87 

9.16 401 

89 

10.83 599 

9.99 543 

42 

8 

11.9 

11.7 

11.6 

19 

9.16 030 

86 

9.16 489 

88 

88 

10.83 511 

9.99 541 

41 

9 

10 

13.4 

14.8 

13.2 

14.7 

13.0 

14.5 

20 

9.16 116 


9.16 577 

10.83 423 

9.99 539 

40 

20 

29.7 

29.3 

29.0 

21 

9.16 203 

87 

9.16 665 

88 

10.83 335 

9.99 537 

39 

30 

44.5 

44.0 

43.5 

22 

9.16 289 

86 

9.16 753 

88 

10.83 247 

9.99 535 

38 

40 

Pin 

59.3 

7/1 O 

58.7 

58.0 

23 

9.16 374 

85 

9.16 841 

88 

10.83 159 

9.99 533 

37 

OU 


73.3 

72.5 

24 

9.16 460 

86 

85 

9.16 928 

87 

88 

10.83 072 

9.99 532 

36 





25 

9.16 545 

9.17 016 

10.82 984 

9.99 530 

35 





26 

9.16 631 

86 

9.17 103 

87 

10.82 897 

9.99 528 

34 

// 

86 

85 

84 

27 

9.16 716 

85 

9.17 190 

87 

10.82 810 

9.99 526 

33 





28 

9.16 801 

85 

9.17 277 

87 

10.82 723 

9.99 524 

32 

6 

8.6 

8.5 

8.4 

29 

9.16 886 

85 

84 

9.17 363 

86 

87 

10.82 637 

9.99 522 

31 

7 

g 

10.0 

lie 

9.9 

1 1 Q 

9.8 

1 1 o 

30 

9.16 970 

9.17 450 

10.82 550 

9.99 520 

30 

9 

X i. .o 

12.9 

11.0 

12.8 

11.^ 

12.6 

31 

9.17 055 

85 

9.17 536 

86 

10.82 464 

9.99 518 

29 

10 

14.3 

14.2 

14.0 

32 

9.17 139 

84 

9.17 622 

86 

10.82 378 

9.99 517 

28 

20 

28.7 

28.3 

28.0 

33 

9.17 223 

84 

9.17 708 

86 

10.82 292 

9.99 515 

27 

30 

43.0 

42.5 

42.0 

34 

9.17 307 

84 

84 

9.17 794 

86 

10.82 206 

9.99 513 

26 

40 

50 

57.3 

71.7 

56.7 

70.8 

56.0 

70.0 

35 

9.17 391 

9.17 880 

oO 

10.82 120 

9.99 511 

25 





36 

9.17 474 

83 

9.17 965 

85 

10.82 035 

9.99 509 

24 





37 

9.17 558 

84 

9.18 051 

86 

10.81 949 

9.99 507 

23 





38 

9.17 641 

83 

9.18 136 

85 

10.81 864 

9.99 505 

22 

n 

83 

82 

81 

39 

9.17 724 

83 

83 

9.18 221 

85 

85 

10.81 779 

9.99 503 

21 


8.3 
9 7 



40 

9.17 807 

9.18 306 

10.81 694 

9.99 501 

20 

6 

7 

8.2 
Q A 

8.1 

41 

9.17 890 

83 

9.18 391 

85 

10.81 609 

9.99 499 

19 

8 

ILl 

y.D 

10.9 

10 8 

42 

9.17 973 

83 

9.18 475 

84 

10.81 525 

9.99 497 

18 

9 

12.4 

12.3 

12.2 

43 

9.18 055 

82 

9.18 560 

85 

10.81 440 

9.99 495 

17 

10 

13.8 

13.7 

13.5 

44 

9.18 137 

82 

83 

9.18 644 

84 

84 

10.81 356 

9.99 494 

16 

20 

30 

27.7 
41 5 

27.3 

41 0 

27.0 

40 5 

45 

9.18 220 

9.18 728 

10.81 272 

9.99 492 

15 

40 

55.3 

54.7 

54^0 

46 

9.18 302 

82 

9.18 812 

84 

10.81 188 

9.99 490 

14 

50 

69.2 

68.3 

67.5 

47 

9.18 383 

81 

9.18 896 

84 

10.81 104 

9.99 488 

13 





48 

9.18 465 

82 

9.18 979 

83 

10.81 021 

9.99 486 

12 





49 

9.18 547 

82 

81 

9.19 063 

84 

83 

10.80 937 

9.99 484 

11 





50 

9.18 628 

9.19 146 

10.80 854 

9.99 482 

10 

" 

80 

2 

1 

51 

9.18 709 

81 

9.19 229 

83 

10.80 771 

9.99 480 

9 

0 

a n 

A O 

n 1 

52 

9.18 790 

81 

9.19 312 

83 

10.80 688 

9.99 478 

8 

7 

o.U 

9 3 

0 2 

U. 1 

0 1 

53 

9.18 871 

81 

9.19 395 

83 

10.80 605 

9.99 476 

7 

8 

10.7 

0.3 

o!i 

54 

9.18 952 

81 

81 

9.19 478 

83 

83 

10.80 522 

9.99 474 

6 

9 

12.0 

0.3 

0.2 

55 

9.19 033 

9.19 561 

10.80 439 

9.99 472 

5 

10 

20 

13.3 
26 7 

0.3 

0 7 

0.2 

0 3 

56 

9.19 113 

80 

9.19 643 

82 

10.80 357 

9.99 470 

4 

30 

40.0 

1.0 

o!5 

57 

9.19 193 

80 

9.19 725 

82 

10.80 275 

9.99 468 

3 

40 

53.3 

1.3 

0.7 

58 

9.19 273 

80 

9.19 807 

82 

10.80 193 

9.99 466 

2 

50 

66.7 

1.7 

0.8 

59 

9.19 353 

80 

9.19 889 

82 

82 

10.80 111 

9.99 464 

1 





60 

9.19 433 

oU 

9.19 971 

10.80 029 

9.99 462 

0 






L Cos 

d 

L Cot 

c d 1 

L Tan 

L Sin 


Prop. Pts. 


81 




















































































36 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


9° 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 


0 

9.19 433 


9.19 971 


10.80 029 

9.99 462 

60 

1 

9.19 513 

80 

9.20 053 

82 

10.79 947 

9.99 460 

59 

2 

9.19 592 

79 

9.20 134 

81 

10.79 866 

9.99 458 

58 

3 

9.19 672 

80 

9.20 216 

82 

10.79 784 

9.99 456 

57 

4 

9.19 751 

79 

79 

9.20 297 

81 

81 

10.79 703 

9.99 454 

56 

5 

9.19 830 

9.20 378 

10.79 622 

9.99 452 

55 

6 

9.19 909 

79 

9.20 459 

81 

10.79 541 

9.99 450 

54 

7 

9.19 988 

79 

9.20 540 

81 

10.79 460 

9.99 448 

53 

8 

9.20 067 

79 

9.20 621 

81 

10.79 379 

9.99 446 

52 

9 

9.20 145 

78 

78 

9.20 701 

80 

81 

10.79 299 

9.99 444 

51 

10 

9.20 223 

9.20 782 

10.79 218 

9.99 442 

50 

11 

9.20 302 

79 

9.20 862 

80 

10.79 138 

9.99 440 

49 

12 

9.20 380 

78 

9.20 942 

80 

10.79 058 

9.99 438 

48 

13 

9.20 458 

78 

9.21 022 

80 

10.78 978 

9.99 436 

47 

14 

9.20 535 

77 

78 

9.21 102 

80 

cn 

10.78 898 

9.99 434 

46 

15 

9.20 613 

9.21 182 

oU 

10.78 818 

9.99 432 

45 

16 

9.20 691 

78 

9.21 261 

79 

10.78 739 

9.99 429 

44 

17 

9.20 768 

77 

9.21 341 

80 

10.78 659 

9.99 427 

43 

18 

9.20 845 

77 

9.21 420 

79 

10.78 580 

9.99 425 

42 

19 

9.20 922 

77 

77 

9.21 499 

79 

79 

10.78 501 

9.99 423 

41 

20 

9.20 999 

9.21 578 

10.78 422 

9.99 421 

40 

21 

9.21 076 

77 

9.21 657 

79 

10.78 343 

9.99 419 

39 

22 

9.21 153 

77 

9.21 736 

79 

10.78 264 

9.99 417 

38 

23 

9.21 229 

76 

9.21 814 

78 

10.78 186 

9.99 415 

37 

24 

9.21 306 

77 

76 

9.21 893 

79 

78 

10.78 107 

9.99 413 

36 

25 

9.21 382 

9.21 971 

10.78 029 

9.99 411 

35 

26 

9.21 458 

76 

9.22 049 

78 

10.77 951 

9.99 409 

34 

27 

9.21 534 

76 

9.22 127 

78 

10.77 873 

9.99 407 

33 

28 

9.21 610 

76 

9.22 205 

78 

10.77 795 

9.99 404 

32 

29 

9.21 685 

75 

76 

9.22 283 

78 

78 

10.77 717 

9.99 402 

31 

30 

9.21 761 

9.22 361 

10.77 639 

9.99 400 

30 

31 

9.21 836 

75 

9.22 438 

77 

10.77 562 

9.99 398 

29 

32 

9.21 912 

76 

9.22 516 

78 

10.77 484 

9.99 396 

28 

33 

9.21 987 

75 

9.22 593 

77 

10.77 407 

9.99 394 

27 

34 

9.22 062 

75 

75 

9.22 670 

77 

77 

10.77 330 

9.99 392 

26 

35 

9.22 137 

9.22 747 

10.77 253 

9.99 390 

25 

36 

9.22 211 

74 

9.22 824 

77 

10.77 176 

9.99 388 

24 

37 

9.22 286 

75 

9.22 901 

77 

10.77 099 

9.99 385 

23 

38 

9.22 361 

75 

9.22 977 

76 

10.77 023 

9.99 383 

22 

39 

9.22 435 

74 

74 

9.23 054 

77 

76 

10.76 946 

9.99 381 

21 

40 

9.22 509 

9.23 130 

10.76 870 

9.99 379 

20 

41 

9.22 583 

74 

9.23 206 

76 

10.76 794 

9.99 377 

19 

42 

9.22 657 

74 

9.23 283 

77 

10.76 717 

9.99 375 

18 

43 

9.22 731 

74 

9.23 359 

76 

10.76 641 

9.99 372 

17 

44 

9.22 805 

74 

73 

9.23 435 

76 

75 

10.76 565 

9.99 370 

16 

45 

9.22 878 

9.23 510 

10.76 490 

9.99 368 

15 

46 

9.22 952 

74 

9.23 586 

76 

10.76 414 

9.99 366 

14 

47 

9.23 025 

73 

9.23 661 

75 

10.76 339 

9.99 364 

13 

48 

9.23 098 

73 

9.23 737 

76 

10.76 263 

9.99 362 

12 

49 

9.23 171 

73 

73 

9.23 812 

75 

75 

10.76 188 

9.99 359 

11 

50 

9.23 244 

9.23 887 

10.76 113 

9.99 357 

10 

51 

9.23 317 

73 

9.23 962 

75 

10.76 038 

9.99 355 

9 

52 

9.23 390 

73 

9.24 037 

75 

10.75 963 

9.99 353 

8 

53 

9.23 462 

72 

9.24 112 

75 

10.75 888 

9.99 351 

7 

54 

9.23 535 

73 

72 

9.24 186 

74 

75 

10.75 814 

9.99 348 

6 

55 

9.23 607 

9.24 261 

10.75 739 

9.99 346 

5 

56 

9.23 679 

72 

9.24 335 

74 

10.75 665 

9 99 344 

4 

57 

9.23 752 

73 

9.24 410 

75 

10.75 590 

y.99 342 

3 

58 

9.23 823 

71 

9.24 484 

74 

10.75 516 

9.99 340 

2 

59 

9.23 895 

72 

72 

9.24 558 

74 

74 

10.75 442 

9.99 337 

1 

60 

9.23 967 

9.24 632 

10.75 368 

9.99 335 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

/ 


Prop. Pts. 


tt 

80 

79 

78 

6 

8.0 

7.9 

7.8 

7 

9.3 

9.2 

9.1 

8 

10.7 

10.5 

10.4 

9 

12.0 

11.8 

11.7 

10 

13.3 

13.2 

13.0 

20 

26.7 

26.3 

26.0 

30 

40.0 

39.5 

39.0 

40 

53.3 

52.7 

52.0 

50 

66.7 

65.8 

65.0 


n 

77 

76 

75 

6 

7.7 

7.6 

7.5 

7 

9.0 

8.9 

8.8 

8 

10.3 

10.1 

10.0 

9 

11.6 

11.4 

11.2 

10 

12.8 

12.7 

12.5 

20 

25.7 

25.3 

25.0 

30 

38.5 

38.0 

37.5 

40 

51.3 

50.7 

50.0 

50 

64.2 

63.3 

62.5 


" 

74 

73 

72 

6 

7.4 

7.3 

7.2 

7 

8.6 

8.5 

8.4 

8 

9.9 

9.7 

9.6 

9 

11.1 

11.0 

10.8 

10 

12.3 

12.2 

12.0 

20 

24.7 

24.3 

24.0 

30 

37.0 

36.5 

36.0 

40 

49.3 

48.7 

48.0 

50 

61.7 

60.8 

60.0 


" 

71 

3 

2 

6 

7.1 

0.3 

0.2 

7 

8.3 

0.4 

0.2 

8 

9.5 

0.4 

0.3 

9 

10.6 

0.4 

0.3 

10 

11.8 

0.5 

0.3 

20 

23.7 

1.0 

0.7 

30 

35.5 

1.5 

1.0 

40 

47.3 

2.0 

1.3 

50 

59.2 

2.5 

1.7 


Prop. Pts. 


80 ' 
































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


37 


10 ° 


' 

L Sin 

d 

L Tan 

c d 

LCot 

L Cos 


Prop. Pts. 

0 

9.23 967 

72 

9.24 632 

74 

10.75 368 

9.99 335 

60 





1 

9.24 039 

9.24 706 

10.75 294 

9.99 333 

59 





2 

9.24 110 

71 

9.24 779 

73 

10.75 221 

9.99 331 

58 





3 

9.24 181 

71 

9.24 853 

74 

10.75 147 

9.99 328 

57 





4 

9.24 253 

72 

71 

9.24 926 

73 

74 

10.75 074 

9.99 326 

56 





5 

9.24 324 

9.25 000 

10.75 000 

9.99 324 

55 


74 

73 

72 

6 

9.24 395 

71 

9.25 073 

73 

10.74 927 

9.99 322 

54 

6 

7 

7.4 
8 6 

7.3 
8 5 

7.2 

8 4 

7 

9.24 466 

71 

9.25 146 

73 

10.74 854 

9.99 319 

53 

8 

9.24 536 

70 

9.25 219 

73 

10.74 781 

9.99 317 

52 

8 

9.9 

9.7 

9^6 

9 

9.24 607 

71 

70 

9.25 292 

73 

73 

10.74 708 

99.9 315 

51 

9 

10 

20 

11.1 
12.3 
24 7 

11.0 
12.2 
24 3 

10.8 

12.0 

24 0 

10 

9.24 677 

9.25 365 

10.74 635 

9.99 313 

50 

11 

9.24 748 

71 

9.25 437 

72 

10.74 563 

9.99 310 

49 

30 

37.0 

36.5 

36.0 

12 

9.24 818 

70 

9.25 510 

73 

10.74 490 

9.99 308 

48 

40 

49.3 

48.7 

48.0 

13 

9.24 888 

70 

9.25 582 

72 

10.74 418 

9.99 306 

47 

50 

61.7 

60.8 

60.0 

14 

9.24 958 

70 

70 

9.25 655 

73 

72 

10.74 345 

9.99 304 

46 





15 

9.25 028 

9.25 727 

10.74 273 

9.99 301 

45 





16 

9.25 098 

70 

9.25 799 

72 

10.74 201 

9.99 299 

44 





17 

9.25 168 

70 

9.25 871 

72 

10.74 129 

9.99 297 

43 





18 

8.25 237 

69 

9.25 943 

72 

10.74 057 

9.99 294 

42 





19 

9.25 307 

70 

9.26 015 

72 

71 

10.73 985 

9.99 292 

41 

» 

71 

70 

69 

20 

9.25 376 


9.26 086 

10.73 914 

9.99 290 

40 

6 

7 

7.1 

8.3 

9.5 

7.0 

8.2 

9.3 

6.9 

8.0 

9.2 

21 

9.25 445 

69 

9.26 158 

72 

10.73 842 

9.99 288 

39 

22 

9.25 514 

69 

9.26 229 

71 

10.73 771 

9.99 285 

38 

8 

23 

9.25 583 

69 

9.26 301 

72 

10.73 699 

9.99 283 

37 

9 

10.6 

10.5 

10.4 

24 

9.25 652 

69 

9.26 372 

71 

10.73 628 

9.99 281 

36 

10 

11.8 

11.7 

11.5 





71 




20 

30 

23.7 
35 5 

23.3 

35.0 

OQ Q 

25 

9.25 721 

ua 

9.26 443 

10.73 557 

9.99 278 

35 

34.5 

26 

9.25 790 

69 

9.26 514 

71 

10.73 486 

9.99 276 

34 

40 

47.3 

46.7 

46.0 

27 

9.25 858 

68 

9.26 585 

71 

10.73 415 

9.99 274 

33 

50 

59.2 

58.3 

57.5 

28 

9.25 927 

69 

9.26 655 

70 

10.73 345 

9.99 271 

32 





29 

9.25 995 

68 

68 

9.26 726 

71 

71 

10.73 274 

9.99 269 

31 





30 

9.26 063 

9.26 797 

4 1 

70 

10.73 203 

9.99 267 

30 





31 

9.26 131 

68 

9.26 867 

10.73 133 

9.99 264 

29 





32 

9.26 199 

68 

9.26 937 

70 

10.73 063 

9.99 262 

28 





33 

9.26 267 

68 

9.27 008 

71 

10.72 992 

9.99 260 

27 

,, 

68 

67 

66 

34 

9.26 335 

68 

9.27 078 

70 

70 

10.72 922 

9.99 257 

26 


35 

9.26 403 

Do 

67 

9.27 148 

10.72 852 

9.99 255 

25 

6 

7 

6.8 
7.9 
9 1 

6.7 

7.8 
8 9 

6.6 

7.7 

8 8 

36 

9.26 470 

9.27 218 

70 

10.72 782 

9.99 252 

24 

4 

8 

37 

9.26 538 

68 

9.27 288 

70 

10.72 712 

9.99 250 

23 

9 

10’2 

lO'.O 

9.9 

38 

9.26 605 

67 

9.27 357 

69 

10.72 643 

9.99 248 

22 

10 

11.3 

11.2 

11.0 

39 

9.26 672 

67 

67 

9.27 427 

70 

RQ 

10.72 573 

9.99 245 

21 

20 

22.7 

22.3 

33.5 

44.7 

22.0 

33.0 

44.0 

40 

9.26 739 

9.27 496 

oy 

70 

10.72 504 

9.99 243 

20 

OU 

40 

45.3 

41 

9.26 806 

67 

9.27 566 

10.72 434 

9.99 24l 

19 

50 

56.7 

55.8 

55.0 

42 

9.26 873 

67 

9.27 635 

69 

10.72 365 

9.99 238 

18 





43 

9.26 940 

67 

9.27 704 

69 

10.72 296 

9.99 236 

17 





44 

9.27 007 

67 

66 

9.27 773 

69 

AQ 

10.72 227 

9.99 233 

16 





45 

9.27 073 

9.27 842 

oy 

10.72 158 

9.99 231 

15 





46 

9.27 140 

67 

9.27 911 

69 

10.72 089 

9.99 229 

14 





47 

9.27 206 

66 

9.27 980 

69 

10.72 020 

9.99 226 

13 

,, 

65 

3 

2 

48 

9.27 273 

67 

9.28 049 

69 

10.71 951 

9.99 224 

12 




49 

9.27 339 

66 

66 

9.28 117 

68 

AQ 

10.71 883 

9.99 221 

11 

6 

6.5 

0.3 

0.2 

50 

9.27 405 

9.28 186 

oy 

68 

10.71 814 

9.99 219 

10 

7 

8 

9 

7.6 

8.7 

9.8 

0.4 

0.4 

0.4 

0.2 

0.3 

0.3 

51 

9.27 471 

66 

9.28 254 

10.71 746 

9.99 217 

9 

52 

9.27 537 

66 

9.28 323 

69 

10.71 677 

9.99 214 

8 

10 

10.8 

0.5 

0.3 

53 

9.27 602 

65 

9.28 391 

68 

10.71 609 

9.99 212 

7 

20 

21.7, 

1.0 

0.7 

54 

9.27 668 

66 

9.28 459 

68 

AS 

10.71 541 

9.99 209 

6 

30 

40 

32.5 

43.3 

54.2 

1.5 
2.0 

2.5 

1.0 

1.3 

1.7 

55 

9.27 734 

66 

9.28 527 

Do 

68 

10.71 473 

9.99 207 

5 

50 

56 

9.27 799 

65 

9.28 595 

10.71 405 

9.99 204 

4 




57 

9.27 864 

65 

9.28 662 

67 

10.71 338 

9.99 202 

3 





58 

9.27 930 

66 

9.28 730 

68 

10.71 270 

9.99 200 

2 





59 

9.27 995 

65 

65 

9.28 798 

68 

67 

10.71 202 

9.99 197 

1 





60 

9.28 060 

9.28 865 

10.71 135 

9.99 195 

0 






L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

' 

Prop. Pts. 


79 ' 
































































38 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


IV 


' 

LSin 

d 

L Tan 

c d 

L Cot 

L Cos 


0 

9.28 060 


9.28 865 


10.71 135 

9.99 195 

60 

1 

9.28 125 

65 

9.28 933 

68 

10.71 067 

9.99 192 

59 

2 

9.28 190 

65 

9.29 000 

67 

10.71 000 

9.99 190 

58 

3 

9.28 254 

64 

9.29 067 

67 

10.70 933 

9.99 187 

57 

4 

9.28 319 

65 

65 

9.29 134 

67 

10.70 866 

9.99 185 

56 

5 

9.28 384 

9.29 201 

D i 

10.70 799 

9.99 182 

55 

6 

9.28 448 

64 

9.29 268 

67 

10.70 732 

9.99 180 

54 

7 

9.28 512 

64 

9.29 335 

67 

10.70 665 

9.99 177 

53 

8 

9.28 577 

65 

9.29 402 

67 

10.70 598 

9.99 175 

52 

9 

9.28 641 

64 

64 

9.29 468 

66 

67 

10.70 532 

9.99 172 

51 

10 

9.28 705 

9.29 535 

10.70 465 

9.99 170 

50 

11 

9.28 769 

64 

9.29 601 

66 

10.70 399 

9.99 167 

49 

12 

9.28 833 

64 

9.29 668 

67 

10.70 332 

9.99 165 

48 

13 

9.28 896 

63 

9.29 734 

66 

10.70 266 

9.99 162 

47 

14 

9.28 960 

64 

64 

9.29 800 

66 

66 

10.70 200 

9.99 160 

46 

15 

9.29 024 

9.29 866 

10.70 134 

9.99 157 

45 

16 

9.29 087 

63 

9.29 932 

66 

10.70 068 

9.99 155 

44 

17 

9.29 150 

63 

9.29 998 

66 

10.70 002 

9.99 152 

43 

18 

9.29 214 

64 

9.30 064 

66 

10.69 936 

9.99 150 

42 

19 

9.29 277 

63 

63 

9.30 130 

66 

65 

10.69 870 

9.99 147 

41 

20 

9.29 340 

9.30 195 

10.69 805 

9.99 145 

40 

21 

9.29 403 

63 

9.30 261 

66 

10.69 739 

9.99 142 

39 

22 

9.29 466 

63 

9.30 326 

65 

10.69 674 

9.99 140 

38 

23 

9.29 529 

63 

9.30 391 

65 

10.69 609 

9.99 137 

37 

24 

9.29 591 

62 

63 

9.30 457 

66 

65 

10.69 543 

9.99 135 

36 

25 

9.29 654 

9.30 522 

10.69 478 

9.99 132 

35 

26 

9.29 716 

62 

9.30 587 

65 

10.69 413 

9.99 130 

34 

27 

9.29 779 

63 

9.30 652 

65 

10.69 348 

9.99 127 

33 

28 

9.29 841 

62 

9.30 717 

65 

10.69 283 

9.99 124 

32 

29 

9.29 903 

62 

63 

9.30 782 

65 

64 

10.69 218 

9.99 122 

31 

30 

9.29 966 

9.30 846 

10.69 154 

9.99 119 

30 

31 

9.30 028 

62 

9.30 911 

65 

10.69 089 

9.99 117 

29 

32 

9.30 090 

62 

9.30 975 

64 

10.69 025 

9.99 114 

28 

33 

9.30 151 

61 

9.31 040 

65 

10.68 960 

9.99 112 

27 

34 

9.30 213 

62 

62 

9.31 104 

64 

64 

10.68 896 

9.99 109 

26 

35 

9.30 275 

9.31 168 

10.68 832 

9.99 106 

25 

36 

9.30 336 

61 

9.31 233 

65 

10.68 767 

9.99 104 

24 

37 

9.30 398 

62 

9.31 297 

64 

10.68 703 

9.99 101 

23 

38 

9.30 459 

61 

9.31 361 

64 

10.68 639 

9.99 099 

22 

39 

9.30 521 

62 

61 

9.31 425 

64 

64 

10.68 575 

9.99 096 

21 

40 

9.30 582 

9.31 489 

10.68 511 

9.99 093 

20 

41 

9.30 643 

61 

9.31 552 

63 

10.68 448 

9.99 091 

19 

42 

9.30 704 

61 

9.31 616 

64 

10.68 384 

9.99 088 

18 

43 

9.30 765 

61 

9.31 679 

63 

10.68 321 

9.99 086 

17 

44 

9.30 826 

61 

61 

9.31 743 

64 

63 

10.68 257 

9.99 083 

16 

45 

9.30 887 

9.31 806 

10.68 194 

9.99 080 

15 

46 

9.30 947 

60 

9.31 870 

64 

10.68 130 

9.99 078 

14 

47 

9.31 008 

61 

9.31 933 

63 

10.68 067 

9.99 075 

13 

48 

9.31 068 

60 

9.31 996 

63 

10.68 004 

9.99 072 

12 

49 

9.31 129 

61 

60 

9.32 059 

63 

63 i 

10.67 941 

9.99 070 

11 

60 

9.31 189 

9.32 122 

10.67 878 

9.99 067 

10 

51 

9.31 250 

61 

9.32 185 

63 1 

10.67 815 

9.99 064 

9 

52 

9.31 310 

60 

9.32 248 

63 

10.67 752 

9.99 062 

8 

53 

9.31 370 

60 

9.32 311 

63 

10.67 689 

9.99 059 

7 

54 

9.31 430 

60 

60 

9.32 373 

62 

63 

10.67 627 

9.99 056 

6 

55 

9.31 490 

9.32 436 

10.67 564 

9.99 054 

5 

56 

9.31 549 

59 

9.32 498 

62 

10.67 502 

9.99 051 

4 

57 

9.31 609 

60 

9.32 561 

63 

10.67 439 

9.99 048 

3 

58 

9.31 669 

60 

9.32 623 

62 

10.67 377 

9.99 046 

2 

59 

9.31 728 

59 

60 

9.32 685 

62 

62 

10.67 315 

9.99 043 

1 

60 

9.31 788 

9.32 747 

10.67 253 

9.99 040 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

' 


Prop. Pts. 



68 

67 

66 

6 

6.8 

6.7 

6.6 

7 

7.9 

7.8 

7.7 

8 

9.1 

8.9 

8.8 

9 

10.2 

10.0 

9.9 

10 

11.3 

11.2 

11.0 

20 

22.7 

22.3 

22.0 

30 

34.0 

33.5 

33.0 

40 

45.3 

44.7 

44.0 

50 

56.7 

55.8 

55.0 



65 

64 

63 

6 

6.5 

6.4 

6.3 

7 

7.6 

7.5 

7.4 

8 

8.7 

8.5 

8.4 

9 

9.8 

9.6 

9.4 

10 

10.8 

10.7 

10.5 

20 

21.7 

21.3 

21.0 

30 

32.5 

32.0 

31.5 

40 

43.3 

42.7 

42.0 

50 

54.2 

53.3 

52.5 


" 

62 

61 

6 

6.2 

6.1 

7 

7.2 

7.1 

8 

8.3 

8.1 

9 

9.3 

9.2 

10 

10.3 

10.2 

20 

20.7 

20.3 

30 

31.0 

30.5 

40 

41.3 

40.7 

50 

51.7 

50.8 


60 

6.0 

7.0 

8.0 

9.0 

10.0 

20.0 

30.0 

40.0 

50.0 



59 

3 

2 

6 

5.9 

0.3 

0.2 

7 

6.9 

0.4 

0.2 

8 

7.9 

0.4 

0.3 

9 

8.8 

0.5 

0.3 

10 

9.8 

0.5 

0.3 

20 

19.7 

1.0 

0.7 

30 

29.5 

1.5 

1.0 

40 

39.3 

2.0 

1.3 

50 

49.2 

2.5 

1.7 


Prop. Pts. 


78 ' 









































































vr 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


39 


12 ' 


/ 

L Sin 

0 

9.31 788 

1 

9.31 847 

2 

9.31 907 

3 

9.31 966 

4 

9.32 025 

5 

9.32 084 

6 

9.32 143 

7 

9.32 202 

8 

9.32 261 

9 

9.32 319 

10 

9.32 378 

11 

9.32 437 

12 

9.32 495 

13 

9.32 553 

14 

9.32 612 

15 

9.32 670 

16 

9.32 728 

17 

9.32 786 

18 

9.32 844 

19 

9.32 902 

20 

9.32 960 

21 

9.33 018 

22 

9.33 075 

23 

9.33 133 

24 

9.33 190 

25 

9.33 248 

26 

9.33 305 

27 

9.33 362 

28 

9.33 420 

29 

9.33 477 

30 

9.33 534 

31 

9.33 591 

32 

9.33 647 

33 

9.33 704 

34 

9.33 761 

35 

9.33 818 

36 

9.33 874 

37 

9.33 931 

38 

9.33 987 

39 

9.34 043 

40 

9.34 100 

41 

9.34 156 

42 

9.34 212 

43 

9.34 268 

44 

9.34 324 

45 

9.34 380 

46 

9.34 436 

47 

9.34 491 

48 

9.34 547 

49 

9.34 602 

50 

9.34 658 

51 

9.34 713 

52 

9.34 769 

53 

9.34 824 

54 

9.34 879 

55 

9.34 934 

56 

9.34 989 

57 

9.35 044 

58 

9.35 099 

59 

9.35 154 

60 

9.35 209 


L Cos 


L Tan 

9.32 

747 

9.32 

810 

9.32 

872 

9.32 

933 

9.32 

995 

9.33 

057 

9.33 

119 

9.33 

180 

9.33 

242 

9.33 

303 

9.33 

365 

9.33 

426 

9.33 

487 

9.33 

548 

9.33 

609 

9.33 

670 

9.33 

731 

9.33 

792 

9.33 

853 

9.33 

913 

9.33 

974 

9.34 

034 

9.34 

095 

9.34 

155 

9.34 

215 

9.34 

276 

9.34 

336 

9.34 

396 

9.34 

456 

9.34 

516 

9.34 

576 

9.34 

635 

9.34 

695 

9.34 

755 

9.34 

814 

9.34 

874 

9.34 

933 

9.34 

992 

9.35 

051 

9.35 

111 

9.35 

170 

9.35 

229 

9.35 

288 

9.35 

347 

9.35 

405 

9.35 

464 

9.35 

523 

9.35 

581 

9.35 

640 

9.35 

698 

9.35 

757 

9.35 

815 

9.35 

873 

9.35 

931 

9.35 

989 

9.36 

047 

9.36 

105 

9.36 

163 

9.36 

221 

9.36 

279 


LCot 

L Cos 


10.67 253 

9.99 040 

60 

10.67 190 

9.99 038 

59 

10.67 128 

9.99 035 

58 

10.67 067 

9.99 032 

57 

10.67 005 

9.99 030 

56 

10.66 943 

9.99 027 

55 

10.66 881 

9.99 024 

54 

10.66 820 

9.99 022 

53 

10.66 758 

9.99 019 

52 

10.66 697 

9.99 016 

51 

10.66 635 

9.99 013 

50 

10.66 574 

9.99 on 

49 

10.66 513 

9.99 008 

48 

10.66 452 

9.99 005 

47 

10.66 391 

9.99 002 

46 

10.66 330 

9.99 000 

45 

10.66 269 

9.98 997 

44 

10.66 208 

9.98 994 

43 

10.66 147 

9.98 991 

42 

10.66 087 

9.98 989 

41 

10.66 026 

9.98 986 

40 

10.65 966 

9.98 983 

39 

10.65 905 

9.98 980 

38 

10.65 845 

9.98 978 

37 

10.65 785 

9.98 975 

36 

10.65 724 

9.98 972 

35 

10.65 664 

9.98 969 

34 

10.65 604 

9.98 967 

33 

10.65 544 

9.98 964 

32 

10.65 484 

9.98 961 

31 

10.65 424 

9.98 958 

30 

10.65 365 

9.98 955 

29 

10.65 305 

9.98 953 

28 

10.65 245 

9.98 950 

27 

10.65 186 

9.98 947 

26 

10.65 126 

9.98 944 

25 

10.65 067 

9.98 941 

24 

10.65 008 

9.98 938 

23 

10.64 949 

9.98 936 

22 

10.64 889 

9.98 933 

21 

10.64 830 

9.98 930 

20 

10.64 771 

9.98 927 

19 

10.64 712 

9.98 924 

18 

10.64 653 

9.98 921 

17 

10.64 595 

9.98 919 

16 

10.64 536 

9.98 916 

15 

10.64 477 

9.98 913 

14 

10.64 419 

9.98 910 

13 

10.64 360 

9.98 907 

12 

10.64 302 

9.98 904 

11 

10.64 243 

9.98 901 

10 

10.64 185 

9.98 898 

9 

10.64 127 

9.98 896 

8 

10.64 069 

9.98 893 

7 

10.64 on 

9.98 890 

6 

10.63 953 

9.98 887 

5 

10.63 895 

9.98 884 

4 

10.63 837 

9.98 881 

3 

10.63 779 

9.98 878 

2 

10.63 721 

9.98 875 

1 

10.63 664 

9.98 872 

0 

L Tan 

LSin 

f 



Prop. 

Pts. 

// 

63 

62 

61 

6 


6.3 


6.2 

6.1 

7 


7.4 


7.2 

7.1 

8 


8.4 


8.3 

8.1 

9 


9.4 


9.3 

9.2 

- 10 

10.5 

10.3 

10.2 

20 

21.0 

20.7 

20.3 

30 

31.5 

31.0 

30.5 

40 

42.0 

41.3 

40.7 

50 

52.5 

51.7 

50.8 

ff 

60 

59 

58 

6 


6.0 


5.9 

5.8 

7 


7.0 


6.9 

6.8 

8 


8.0 


7.9 

7.7 

9 


9.0 


8.8 

8.7 

10 

10.0 


9.8 

9.7 

- 20 

20.0 

19.7 

19.3 

30 

30.0 

29.5 

29.0 

40 

40.0 

39.3 

38.7 

50 

50.0 

49.2 

48.3 

n 

57 

56 

55 

6 


5.7 


5.6 

5.5 

7 


6.6 


6.5 

6.4 

8 


7.6 


7.5 

7.3 

9 


8.6 


8.4 

8.2 

10 


9.5 


9.3 

9.2 

20 

19.0 

18.7 

18.3 

30 

28.5 

28.0 

27.5 

40 

38.0 

37.3 

36.7 

50 

47.5 

46.7 

45.8 

tt 

3 


2 



6 

0.3 

0.2 


7 

0.4 

0.2 

8 

0.4 

0.3 


9 

0.5 

0.3 

10 

0.5 

0.3 

20 

1 . 

3 

0.7 

30 

1.5 

1.0 

40 

2.0 

1.3 

50 

2.5 

1.7 


59 

60 
59 
59 
59 

59 

59 

59 

58 

59 

59 

58 

58 

59 
58 

58 

58 

58 

58 

58 

58 

57 

58 

57 

58 
57 

57 

58 
57 
57 

57 

56 

57 
57 
57 

56 

57 
56 

56 

57 

56 

56 

56 

56 

56 

56 

55 

56 

55 

56 

55 

56 
55 
55 
55 

55 

55 

55 

55 

55 


9.36 336 


63 

62 

61 

62 

62 

62 

61 

62 

61 

62 

61 

61 

61 

61 

61 

61 

61 

61 

60 

61 

60 

61 

60 

60 

61 

60 

60 

60 

60 

60 

59 

60 
60 

59 

60 
59 
59 

59 

60 
59 

59 

59 

59 

58 

59 
59 

58 

59 

58 

59 

58 

58 

58 

58 

58 

58 

58 

58 

58 

57 


L Cot I c d 


Pron. Pts. 


77 ° 






















































































































40 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


13 ^ 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 


0 

9.35 209 


9.36 336 


10.63 664 

9.98 872 

60 

1 

9.35 263 

54 

9.36 394 

58 

10.63 606 

9.98 869 

59 

2 

9.35 318 

55 

9.36 452 

58 

10.63 548 

9.98 867 

58 

3 

9.35 373 

55 

9.36 509 

57 

10.63 491 

9.98 864 

57 

4 

9.35 427 

54 

54 

9.36 566 

57 

58 

10.63 434 

9.98 861 

56 

5 

9.35 481 

9.36 624 

10.63 376 

9.98 858 

55 

6 

9.35 536 

55 

9.36 681 

57 

10.63 319 

9.98 855 

54 

7 

9.35 590 

54 

9.36 738 

57 

10.63 262 

9.98 852 

53 

8 

9.35 644 

54 

9.36 795 

57 

10.63 205 

9.98 849 

52 

9 

9.35 698 

54 

54 

9.36 852 

57 

57 

10.63 148 

9.98 846 

51 

10 

9.35 752 

9.36 909 

10.63 091 

9.98 843 

50 

11 

9.35 806 

54 

9.36 966 

57 

10.63 034 

9.98 840 

49 

12 

9.35 860 

54 

9.37 023 

57 

10.62 977 

9.98 837 

48 

13 

9.35 914 

54 

9.37 080 

57 

10.62 920 

9.98 834 

47 

14 

9.35 968 

54 

54 

9.37 137 

57 

56 

10.62 863 

9.98 831 

46 

15 

9.36 022 

9.37 193 

10.62 807 

9.98 828 

45 

16 

9.36 075 

53 

9.37 250 

57 

10.62 750 

9.98 825 

44 

17 

9.36 129 

54 

9.37 306 

56 

10.62 694 

9.98 822 

43 

18 

9.36 182 

53 

9.37 363 

57 

10.62 637 

9.98 819 

42 

19 

9.36 236 

54 

53 

9.37 419 

56 

10.62 581 

9.98 816 

41 

20 

9.36 289 

9.37 476 

0 i 

10.62 524 

9.98 813 

40 

21 

9.36 342 

53 

9.37 532 

56 

10.62 468 

9.98 810 

39 

22 

9.36 395 

53 

9.37 588 

56 

10.62 412 

9.98 807 

38 

23 

9.36 449 

54 

9.37 644 

56 

10.62 356 

9.98 804 

37 

24 

9.36 502 

53 

53 

9.37 700 

56 

10.62 300 

9.98 801 

36 

25 

9.36 555 

9.37 756 

oo 

10.62 244 

9.98 798 

35 

26 

9.36 608 

53 

9.37 812 

56 

10.62 188 

9.98 795 

34 

27 

9.36 660 

52 

9.37 868 

56 

10.62 132 

9.98 792 

33 

28 

9.36 713 

53 

9.37 924 

56 

10.62 076 

9.98 789 

32 

29 

9.36 766 

53 

53 

9.37 980 

56 

10.62 020 

9.98 786 

31 

30 

9.36 819 

9.38 035 

OO 

10.61 965 

9.98 783 

30 

31 

9.36 871 

52 

9.38 091 

56 

10.61 909 

9.98 780 

29 

32 

9.36 924 

53 

9.38 147 

56 

10.61 853 

9.98 777 

28 

33 

9.36 976 

52 

9.38 202 

55 

10.61 798 

9.98 774 

27 

34 

9.37 028 

52 

53 

9.38 257 

55 

56 

10.61 743 

9.98 771 

26 

35 

9.37 081 

9.38 313 

10.61 687 

9.98 768 

25 

36 

9.37 133 

52 

9.38 368 

55 

10.61 632 

9.98 765 

24 

37 

9.37 185 

52 

9.38 423 

55 

10.61 577 

9.98 762 

23 

38 

9.37 237 

52 

9.38 479 

56 

10.61 521 

9.98 759 

22 

39 

9.37 289 

52 

52 

9.38 534 

55 

55 

10.61 466 

9.98 756 

21 

40 

9.37 341 

9.38 589 

10.61 411 

9.98 753 

20 

41 

9.37 393 

52 

9.38 644 

55 

10.61 356 

9.98 750 

19 

42 

9.37 445 

52 

9.38 699 

55 

10.61 301 

9.98 746 

18 

43 

9.37 497 

52 

9.38 754 

55 

10.61 246 

9.98 743 

17 

44 

9.37 549 

52 

51 

9.38 808 

54 

10.61 192 

9.98 740 

16 

45 

9.37 600 

9.38 863 

OO 

10.61 137 

9.98 737 

15 • 

46 

9.37 652 

52 

9.38 918 

55 

10.61 082 

9.98 734 

14 

47 

9.37 703 

51 

9.38 972 

54 

10.61 028 

9.98 731 

13 

48 

9.37 755 

52 

9.39 027 

55 

10.60 973 

9.98 728 

12 

49 

9.37 806 

51 

52 

9.39 082 

55 

54 

10.60 918 

9.98 725 

11 

50 

9.37 858 

9.39 136 

10.60 864 

9.98 722 

10 

51 

9.37 909 

51 

9.39 190 

54 

10.60 810 

9.98 719 

9 

52 

9.37 960 

51 

9.39 245 

55 

10.60 755 

9.98 715 

8 

53 

9.38 on 

51 

9.39 299 

54 

10.60 701 

9.98 712 

7 

54 

9.38 062 

51 

51 

9.39 353 

54 

54 

10.60 647 

9.98 709 

6 

55 

9.38 113 

9.39 407 

10.60 593 

9.98 706 

5 

56 

9.38 164 

51 

9.39 461 

54 

10.60 539 

9.98 703 

4 

57 

9.38 215 

51 

9.39 515 

54 

10.60 485 

9.98 700 

3 

58 

9.38 266 

51 

9.39 569 

54 

10.60 431 

9.98 697 

2 

59 

9.38 317 

51 

51 

9.39 623 

54 

54 

10.60 377 

9.98 694 

1 

60 

9.38 368 

9.39 677 

10.60 323 

9.98 690 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

' 


Prop. Pts. 


" 

58 

57 

56 

6 

5.8 

5.7 

5.6 

7 

6.8 

6.6 

6.5 

8 

7.7 

7.6 

7.5 

9 

8.7 

8.6 

8.4 

10 

9.7 

9.5 

9.3 

20 

19.3 

19.0 

18.7 

30 

29.0 

28.5 

28.0 

40 

38.7 

38.0 

37.3 

50 

48.3 

47.5 

46.7 



55 

54 

53 

6 

5.5 

5.4 

5.3 

7 

6.4 

6.3 

6.2 

8 

7.3 

7.2 

7.1 

9 

8.2 

8.1 

8.0 

10 

9.2 

9.0 

8.8 

20 

18.3 

18.0 

17.7 

30 

27.5 

27.0 

26.5 

40 

36.7 

36.0 

35.3 

50 

45.8 

45.0 

44.2 


" 

52 

51 

4 

6 

5.2 

5.1 

0.4 

7 

6.1 

6.0 

0.5 

8 

6.9 

6.8 

0.5 

9 

7.8 

7.6 

0.6 

10 

8.7 

8.5 

0.7 

20 

17.3 

17.0 

1.3 

30 

26.0 

25.5 

2.0 

40 

34.7 

34.0 

2.7 

50 

43.3 

42.5 

3.3 


0.2 

0.2 

0.3 

0.3 

0.3 

0.7 

1.0 

1.3 

1.7 


Prop. Pts. 


76 ' 





























































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


41 


14 ^ 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 


0 

9.38 368 


9.39 677 


10.60 323 

9.98 690 

60 

1 

9.38 418 

50 

9.39 731 

54 

10.60 269 

9.98 687 

59 

2 

9.38 469 

51 

9.39 785 

54 

10.60 215 

9.98 684 

58 

3 

9.38 519 

50 

9.39 838 

53 

10.60 162 

9.98 681 

57 

4 

9.38 570 

51 

9.39 892 

54 

10.60 108 

9.98 678 

56 

5 

9.38 620 

ou 

9.39 945 

Oo 

10.60 055 

9.98 675 

55 

6 

9.38 670 

50 

9.39 999 

54 

10.60 001 

9.98 671 

54 

7 

9.38 721 

51 

9.40 052 

53 

10.59 948 

9.98 668 

53 

8 

9.38 771 

50 

9.40 106 

54 

10.59 894 

9.98 665 

52 

9 

9.38 821 

50 

9.40 159 

53 

53 

10.59 841 

9.98 662 

51 

10 

9.38 871 

ou 

9.40 212 

10.59 788 

9.98 659 

50 

11 

9.38 921 

50 

9.40 266 

54 

10.59 734 

9.98 656 

49 

12 

9.38 971 

50 

9.40 319 

53 

10.59 681 

9.98 652 

48 

13 

9.39 021 

50 

9.40 372 

53 

10.59 628 

9.98 649 

47 

14 

9.39 071 

50 

9.40 425 

53 

10.59 575 

9.98 646 

46 

15 

9.39 121 


9.40 478 

Oo 

10.59 522 

9.98 643 

45 

16 

9.39 170 

49 

9.40 531 

53 

10.59 469 

9.98 640 

44 

17 

9.39 220 

50 

9.40 584 

53 

10.59 416 

9.98 636 

43 

18 

9.39 270 

50 

9.40 636 

52 

10.59 364 

9.98 633 

42 

19 

9.39 319 

49 

9.40 689 

53 

10.59 311 

9.98 630 

41 

20 

9.39 369 

ou 

9.40 742 

Oo 

10.59 258 

9.98 627 

40 

21 

9.39 418 

49 

9.40 795 

53 

10.59 205 

9.98 623 

39 

22 

9.39 467 

49 

9.40 847 

52 

10.59 153 

9.98 620 

38 

23 

9.39 517 

50 

9.40 900 

53 

10.59 100 

9.98 617 

37 

24 

9.39 566 

49 

9.40 952 

52 

10.59 048 

9.98 614 

36 





53 




25 

9.39 615 


9.41 005 

10.58 995 

9.98 610 

35 

26 

9.39 664 

49 

9.41 057 

52 

10.58 943 

9.98 607 

34 

27 

9.39 713 

49 

9.41 109 

52 

10.58 891 

9.98 604 

33 

28 

9.39 762 

49 

9.41 161 

52 

10.58 839 

9.98 601 

32 

29 

9.39 811 

49 

A Q 

9.41 214 

53 

10.58 786 

9.98 597 

31 

30 

9.39 860 

■ly 

9.41 266 


10.58 734 

9.98 594 

30 

31 

9.39 909 

49 

9.41 318 

52 

10.58 682 

9.98 591 

29 

32 

9.39 958 

49 

9.41 370 

52 

10.58 630 

9.98 588 

28 

33 

9.40 006 

48 

9.41 422 

52 

10.58 578 

9.98 584 

27 

34 

9.40 055 

49 

48 

9.41 474 

52 

fCO 

10.58 526 

9.98 581 

26 

35 

9.40 103 

9.41 526 


10.58 474 

9.98 578 

25 

36 

9.40 152 

49 

9.41 578 

52 

10.58 422 

9.98 574 

24 

37 

9.40 200 

48 

9.41 629 

51 

10.58 371 

9.98 571 

23 

38 

9.40 249 

49 

9.41 681 

52 

10.58 319 

9.98 568 

22 

39 

9.40 297 

48 

A fi 

9.41 733 

52 

10.58 267 

9.98 565 

21 

40 

9.40 346 

4y 

9.41 784 

Oi 

10.58 216 

9.98 561 

20 

41 

9.40 394 

48 

9.41 836 

52 

10.58 164 

9.98 558 

19 

42 

9.40 442 

48 

9.41 887 

51 

10.58 113 

9.98 555 

18 

43 

9.40 490 

48 

9.41 939 

52 

10.58 061 

9.98 551 

17 

44 

9.40 538 

48 

A Q 

9.41 990 

51 

10.58 010 

9.98 548 

16 

45 

9.40 586 

40 

9.42 041 

01 

10.57 959 

9.98 545 

15 

46 

9.40 634 

48 

9.42 093 

52 

10.57 907 

9.98 541 

14 

47 

9.40 682 

48 

9.42 144 

51 

10.57 856 

9.98 538 

13 

48 

9.40 730 

48 

9.42 195 

51 

10.57 805 

9.98 535 

12 

49 

9.40 778 

48 

9.42 246 

51 

1 

10.57 754 

9.98 531 

11 

50 

9.40 825 

47 

9.42 297 

Oi 

10.57 703 

9.98 528 

10 

51 

9.40 873 

48 

9.42 348 

51 

10.57 652 

9.98 525 

9 

52 

9.40 921 

48 

9.42 399 

51 

10.57 601 

9.98 521 

8 

53 

9.40 968 

47 

9.42 450 

51 

10.57 550 

9.98 518 

7 

54 

9.41 016 

48 

9.42 501 

51 

p;i 

10.57 499 

9.98 515 

6 

55 

9.41 063 

47 

9.42 552 

01 

10.57 448 

9.98 511 

5 

56 

9.41 111 

48 

9.42 603 

51 

10.57 397 

9.98 508 

4 

57 

9.41 158 

47 

9.42 653 

50 

10.57 347 

9.98 505 

3 

58 

9.41 205 

47 

9.42 704 

51 

10.57 296 

9.98 501 

2 

59 

9.41 252 

47 

9.42 755 

51 

10.57 245 

9.98 498 

1 

60 

9.41 300 

48 

9.42 805 

ou 

10.57 195 

9.98 494 

0 


L Cos 

! d 

L Cot 

c d 

L Tan 

L Sin 



Prop. Pts. 



54 

53 

52 

6 

5.4 

5.3 

5.2 

7 

6.3 

6.2 

6.1 

8 

7.2 

7.1 

6.9 

9 

8.1 

8.0 

7.8 

10 

9.0 

8.8 

8.7 

20 

18.0 

17.7 

17.3 

30 

27.0 

26.5 

26.0 

40 

36.0 

35.3 

34.7 

50 

45.0 

44.2 

43.3 


" 

51 

50 

49 

6 

5.1 

5.0 

4.9 

7 

6.0 

5.8 

5 ." 

8 

6.8 

6.7 

6.5 

9 

7.6 

7.5 

7.4 

10 

8.5 

8.3 

8.2 

20 

17.0 

16.7 

16.3 

30 

25.5 

25.0 

24.5 

40 

34.0 

33.3 

32.7 

50 

42.5 

41.7 

40.8 


48 

4.8 

5.6 

6.4 

7.2 

8.0 

16.0 

24.0 

32.0 

40.0 


0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


47 

4.7 

5.5 
6.3 
7.0 

7.8 
15.7 

23.5 
31.3 
39.2 


0.3 

0.4 

0.4 

0.4 

0.5 

1.0 

1.5 
2.0 

2.5 


Prop. Pts. 


75 ' 




































































42 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


15 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.41 300 


9.42 805 


10.57 195 

9.98 494 


60 

1 

9.41 347 

47 

9.42 856 

.51 

10.57 144 

9.98 491 

3 

59 

2 

9.41 394 

47 

9.42 906 

50 

10.57 094 

9.98 488 

3 

58 

3 

9.41 441 

47 

9.42 957 

51 

10.57 043 

9.98 484 

4 

57 

4 

9.41 488 

47 

47 

9.43 007 

50 

50 

10.56 993 

9.98 481 

3 

4 

56 

5 

9.41 535 

9.43 057 

10.56 943 

9.98 477 


55 

6 

9.41 582 

47 

9.43 108 

51 

10.56 892 

9.98 474 

3 

54 

7 

9.41 628 

46 

9.43 158 

50 

10.56 842 

9.98 471 

3 

53 

8 

9.41 675 

47 

9.43 208 

50 

10.56 792 

9.98 467 

4 

52 

9 

9.41 722 

47 

46 

9.43 258 

50 

50 

10.56 742 

9.98 464 

3 

A 

51 

10 

9.41 768 

9.43 308 

10.56 692 

9.98 460 


60 

11 

9.41 815 

47 

9.43 358 

50 

10.56 642 

9.98 457 

3 

49 

12 

9.41 861 

46 

9.43 408 

50 

10.56 592 

9.98 453 

4 

48 

13 

9.41 908 

47 

9.43 458 

50 

10.56 542 

9.98 450 

3 

47 

14 

9.41 954 

46 

47 

9.43 508 

50 

50 

10.56 492 

9.98 447 

3 

A 

46 

15 

9.42 001 

9.43 558 

10.56 442 

9.98 443 


45 

16 

9.42 047 

46 

9.43 607 

49 

10.56 393 

9.98 440 

3 

44 

17 

9.42 093 

46 

9.43 657 

50 

10.56 343 

9.98 436 

4 

43 

18 

9.42 140 

47 

9.43 707 

50 

10.56 293 

9.98 433 

3 

42 

19 

9.42 186 

46 

46 

9.43 756 

49 

50 

10.56 244 

9.98 429 

4 

Q 

41 

20 

9.42 232 

9.43 806 

10.56 194 

9.98 426 

o 

40 

21 

9.42 278 

46 

9.43 855 

49 

10.56 145 

9.98 422 

4 

39 

22 

9.42 324 

46 

9.43 905 

50 

10.56 095 

9.98 419 

3 

38 

23 

9.42 370 

46 

9.43 954 

49 

10.56 046 

9.98 415 

4 

37 

24 

9.42 416 

46 

45 

9.44 004 

50 

49 

10.55 996 

9.98 412 

3 

Q 

36 

25 

9.42 461 

9.44 053 

10.55 947 

9.98 409 

O 

35 

26 

9.42 507 

46 

9.44 102 

49 

10.55 898 

9.98 405 

4 

34 

27 

9.42 553 

46 

9.44 151 

49 

10.55 849 

9.98 402 

3 

33 

28 

9.42 599 

46 

9.44 201 

50 

10.55 799 

9.98 398 

4 

32 

29 

9.42 644 

45 

46 

9.44 250 

49 

49 

10.55 750 

9.98 395 

3 

A 

31 

30 

9.42 690 

9.44 299 


10.55 701 

9.98 391 


30 

31 

9.42 735 

45 

9.44 348 

49 

10.55 652 

9.98 388 

3 

29 

32 

9.42 781 

46 

9.44 397 

49 

10.55 603 

9.98 384 

4 

28 

33 

9.42 826 

45 

9.44 446 

49 

10.55 554 

9.98 381 

3 

27 

34 

9.42 872 

46 

45 

9.44 495 

49 

49 

10.55 505 

9.98 377 

4 

26 

35 

9.42 917 

9.44 544 

10.55 456 

9.98 373 


25 

36 

9.42 962 

45 

9.44 592 

48 

10.55 408 

9.98 370 

3 

24 

37 

9.43 008 

46 

9.44 641 

49 

10.55 359 

9.98 366 

4 

23 

38 

9.43 053 

45 

9.44 690 

49 

10.55 310 

9.98 363 

3 

22 

39 

9.43 098 

45 

45 

9.44 738 

48 

49 

10.55 262 

9.98 359 

4 

Q 

21 

40 

9.43 143 

9.44 787 

10.55 213 

9.98 356 

o 

20 

41 

9.43 188 

45 

9.44 836 

49 

10.55 164 

9.98 352 

4 

19 

42 

9.43 233 

45 

9.44 884 

48 

10.55 116 

9.98 349 

3 

18 

43 

9.43 278 

45 

9.44 933 

49 

10.55 067 

9.98 345 

4 

17 

44 

9.43 323 

45 

44 

9.44 981 

48 

as 

10.55 019 

9.98 342 

3 

A 

16 

45 

9.43 367 

9.45 029 


10.54 971 

9.98 338 


15 

46 

9.43 412 

45 

9.45 078 

49 

10.54 922 

9.98 334 

4 

14 

47 

9.43 457 

45 

9.45 126 

48 

10.54 874 

9.98 331 

3 

13 

48 

9.43 502 

45 

9.45 174 

48 

10.54 826 

9.98 327 

4 

12 

49 

9.43 546 

44 

9.45 222 

48 

10.54 778 

9.98 324 

3 

11 



45 


49 





50 

9.43 591 

9.45 271 

10.54 729 

9.98 320 


10 

51 

9.43 635 

44 

9.45 319 

48 

10.54 681 

9.98 317 

3 

9 

52 

9.43 680 

45 

9.45 367 

48 

10.54 633 

9.98 313 

4 

8 

53 

9.43 724 

44 

9.45 415 

48 

10.54 585 

9.98 309 

4 

7 

54 

9.43 769 

45 

44 

9.45 463 

48 

48 

10.54 537 

9.98 306 

3 

A 

6 

55 

9.43 813 

9.45 511 

10.54 489 

9.98 302 

4 

5 

56 

9.43 857 

44 

9.45 559 

48 

10.54 441 

9.98 299 

3 

4 

57 

9.43 901 

44 

9.45 606 

47 

10.54 394 

9.98 295 

4 

3 

58 

9.43 946 

45 

9.45 654 

48 

10.54 346 

9.98 291 

4 

2 

59 

9.43 990 

44 

44 

9.45 702 

48 

48 

10.54 298 

9.98 288 

3 

A 

1 

60 

9.44 034 

9.45 750 

10.54 250 

9.98 284 

4 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 1 

d 

' 


Prop. Pts. 


51 

50 

49 

5.1 

5.0 

4.9 

6.0 

5.8 

5.7 

6.8 

6.7 

6.5 

7.7 

7.5 

7.4 

8.5 

8.3 

8.2 

17.0 

16.7 

16.3 

25.5 

25.0 

24.5 

34.0 

33.3 

32.7 

42.5 

41.7 

40.8 


" 

48 

47 

46 

6 

4.8 

4.7 

4.6 

7 

5.6 

5.5 

5.4 

8 

6.4 

6.3 

6.1 

9 

7.2 

7.0 

6.9 

10 

8.0 

7.8 

7.7 

20 

16.0 

15.7 

15.3 

30 

24.0 

23.5 

23.0 

40 

32.0 

31.3 

30.7 

50 

40.0 

39.2 

38.3 


45 

4.5 
5.3 
6.0 
6.8 

7.5 
15.0 
22.5 


44 

4.4 

5.1 

5.9 

6.6 

7.3 

14.7 

22.0 


30.0 29.3 
37 . 5 | 36.7 


0.3 

0.4 

0.4 

0.5 

0.5 

1.0 

1.5 
2.0 

2.5 


Prop. Pts. 


74 ' 


















































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


43 


16 ^ 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.44 034 


9.45 750 


10.54 250 

9.98 284 


60 

1 

9.44 078 

44 

9.45 797 

47 

10.54 203 

9.98 281 

3 

59 

2 

9.44 122 

44 

9.45 845 

48 

10.54 155 

9.98 277 

4 

58 

3 

9.44 166 

44 

9.45 892 

47 

10.54 108 

9.98 273 

4 

57 

4 

9.44 210 

44 

43 

9.45 940 

48 

47 

10.54 060 

9.98 270 

3 

A 

56 

5 

9.44 253 

9.45 987 

10.54 013 

9.98 266 


55 

6 

9.44 297 

44 

9.46 035 

48 

10.53 965 

9.98 262 

4 

54 

7 

9.44 341 

44 

9.46 082 

47 

10.53 918 

9.98 259 

3 

53 

8 

9.44 385 

44 

9.46 130 

48 

10.53 870 

9.98 255 

4 

52 

9 

9.44 428 

43 

44 

9.46 177 

47 

47 

10.53 823 

9.98 251 

4 

51 

10 

9.44 472 

9.46 224 

10.53 776 

9.98 248 

o 

50 

11 

9.44 516 

44 

9.46 271 

47 

10.53 729 

9.98 244 

4 

49 

12 

9.44 559 

43 

9.46 319 

48 

10.53 681 

9.98 240 

4 

48 

13 

9.44 602 

43 

9.46 366 

47 

10.53 634 

9.98 237 

3 

47 

14 

9.44 646 

44 

43 

9.46 413 

47 

47 

10.53 587 

9.98 233 

4 

A 

46 

15 

9.44 689 

9.46 460 

10.53 540 

9.98 229 

% 

45 

16 

9.44 733 

44 

9.46 507 

47 

10.53 493 

9.98 226 

3 

44 

17 

9.44 776 

43 

9.46 554 

47 

10.53 446 

9.98 222 

4 

43 

18 

9.44 819 

43 

9.46 601 

47 

10.53 399 

9.98 218 

4 

42 

19 

9.44 862 

43 

9.46 648 

47 

10.53 352 

9.98 215 

3 

A. 

41 

20 

9.44 905 


9.46 694 


10.53 306 

9.98 211 


40 

21 

9.44 948 

43 

9.46 741 

47 

10.53 259 

9.98 207 

4 

39 

22 

9.44 992 

44 

9.46 788 

47 

10.53 212 

9.98 204 

3 

38 

23 

9.45 035 

43 

9.46 835 

47 

10.53 165 

9.98 200 

4 

37 

24 

9.45 077 

42 

9.46 881 

46 

10.53 119 

9.98 196 

4 

4 

36 

25 

9.45 120 


9.46 928 

‘il 

10.53 072 

9.98 192 


35 

26 

9.45 163 

43 

9.46 975 

47 

10.53 025 

9.98 189 

3 

34 

27 

9.45 206 

43 

9.47 021 

46 

10.52 979 

9.98 185 

4 

33 

28 

9.45 249 

43 

9.47 068 

47 

10.52 932 

9.98 181 

4 

32 

29 

9.45 292 

43 

AO 

9.47 114 

46 

Af\ 

10.52 886 

9.98 177 

4 

3 

31 

30 

9.45 344 


9.47 160 


10.52 840 

9.98 174 


30 

31 

9.45 377 

43 

9.47 207 

47 

10.52 793 

9.98 170 

4 

29 

32 

9.45 419 

42 

9.47 253 

46 

10.52 747 

9.98 166 

4 

28 

33 

9.45 462 

43 

9.47 299 

46 

10.52 701 

9.98 162 

4 

27 

34 

9.45 504 

42 

A Q 

9.47 346 

47 

10.52 654 

9.98 159 

3 

4 

26 

35 

9.45 547 


9.47 392 


10.52 608 

9.98 155 


25 

36 

9.45 589 

42 

9.47 438 

46 

10.52 562 

9.98 151 

4 

24 

37 

9.45 632 

43 

9.47 484 

46 

10.52 516 

9.98 147 

4 

23 

38 

9.45 674 

42 

9.47 530 

46 

10.52 470 

9.98 144 

3 

22 

39 

9.45 716 

42 

A O 

9.47 576 

46 

AR 

10.52 424 

9.98 140 

; 4 

4 

21 

40 

9.45 758 


9.47 622 

■10 

10.52 378 

9.98 136 


20 

41 

9.45 801 

43 

9.47 668 

46 

10.52 332 

9.98 132 

4 

19 

42 

9.45 843 

42 

9.47 714 

46 

10.52 286 

9.98 129 

3 

18 

43 

9.45 885 

42 

9.47 760 

46 

10.52 240 

9.98 125 

4 

17 

44 

9.45 927 

42 

A O 

9.47 806 

46 

10.52 194 

9.98 121 

4 

4 

16 

45 

9.45 969 


9.47 852 

lO 

10.52 148 

9.98 117 


15 

46 

9.46 011 

42 

9.47 897 

45 

10.52 103 

9.98 113 

4 

14 

47 

9.46 053 

42 

9.47 943 

46 

10.52 057 

9.98 no 

3 

13 

48 

9.46 095 

42 

9.47 989 

46 

10.52 011 

9.98 106 

4 

12 

49 

9.46 136 

41 

A O 

9.48 035 

46 

4,c 

10.51 965 

9.98 102 

4 

4 

11 

50 

9.46 178 


9.48 080 


10.51 920 

9.98 098 


10 

51 

9.46 220 

42 

9.48 126 

46 

10.51 874 

9.98 094 

4 

9 

52 

9.46 262 

42 

9.48 171 

45 

10.51 829 

9.98 090 

4 

8 

53 

9.46 303 

41 

9.48 217 

46 

10.51 783 

9.98 087 

3 

7 

54 

9.46 345 

42 

9.48 262 

45 

AK 

10.51 738 

9.98 083 

4 

4 

6 

55 

9.46 386 

41 

9.48 307 


10.51 693 

9.98 079 


5 

56 

9.46 428 

42 

9.48 353 

46 

10.51 647 

9.98 075 

4 

A 

4 

57 

9.46 469 

41 

9.48 398 

45 

10.51 602 

9.98 071 

4 

A 

3 

58 

9.46 511 

42 

9.48 443 

45 

10.51 557 

9.98 067 

4 

2 

59 

9.46 552 

41 

9.48 489 

46 

A ft 

10.51 511 

9.98 063 

4 

3 

1 

60 

9.46 594 

42 

9.48 534 

lo 

10.51 466 

9.98 060 


0 


L Cos 

d 

LCot 

c d 

L Tan 

L Sin 

d 



Prop. Pts. 



48 

47 

6 

4.8 

4.7 

7 

5.6 

5.5 

8 

6.4 

6.3 

9 

7.2 

7.0 

10 

8.0 

7.8 

20 

16.0 

15.7 

30 

24.0 

23.5 

40 

32.0 

31.3 

50 

40.0 

39.2 


46 

4.6 
5.4 
6.1 
6.9 

7.7 

15.3 
23.0 
30.7 

38.3 



45 

44 

43 

6 

4.5 

4.4 

4.3 

7 

5.3 

5.1 

5.0 

8 

6.0 

5.9 

5.7 

9 

6.8 

6.6 

6.4 

10 

7.5 

7.3 

7.2 

20 

15.0 

14.7 

14.3 

30 

22.5 

22.0 

21.5 

40 

30.0 

29.3 

28.7 

50 

37.5 

36.7 

35.8 


42 

4.2 
4.9 
5.6 

6.3 
7.0 

14.0 

21.0 

28.0 

35.0 


0.4 

0.5 

0.5 

0.6 

0.7 

1.3 
2.0 
2.7 

3.3 


41 

4.1 

4.8 
5.5 

6.2 

6.8 
13.7 
20.5 
27.3 
34.2 


0.3 

0.4 

0.4 

0.5 

0.5 

1.0 

1.5 
2.0 

2.5 


Prop. Pts. 


73 ' 















































































44 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


17 ' 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 



0 

9.46 594 


9.48 534 


10.51 466 

9.98 060 


60 


1 

9.46 635 

41 

9.48 579 

45 

10.51 421 

9.98 056 

4 

59 


2 

9.46 676 

41 

9.48 624 

45 

10.51 376 

9.98 052 

4 

58 


3 

9.46 717 

41 

9.48 669 

45 

10.51 331 

9.98 048 

4 

57 


4 

9.46 758 

41 

42 

9.48 714 

45 

45 

10.51 286 

9.98 044 

4 

A 

56 


5 

9.46 800 

9.48 759 

10.51 241 

9.98 040 


55 


6 

9.46 841 

41 

9.48 804 

45 

10.51 196 

9.98 036 

4 

54 

A 

7 

9.46 882 

41 

9.48 849 

45 

10.51 151 

9.98 032 

4 

53 

U 

7 

8 

9.46 923 

41 

9.48 894 

45 

10.51 106 

9.98 029 

3 

52 

8 

9 

9.46 964 

41 

41 

9.48 939 

45 

45 

10.51 061 

9.98 025 

4 

A 

51 

9 

10 

9.47 005 

9.48 984 

10.51 016 

9.98 021 


50 

10 

20 

11 

9.47 045 

40 

9.49 029 

45 

10.50 971 

9.98 017 

4 

49 

30 

12 

9.47 086 

41 

9.49 073 

44 

10.50 927 

9.98 013 

4 

48 

40 

13 

9.47 127 

41 

9.49 118 

45 

10.50 882 

9.98 009 

4 

47 

50 

14 

9.47 168 

41 

41 

9.49 163 

45 

44 

10.50 837 

9.98 005 

4 

A 

46 


15 

9.47 209 

9.49 207 

10.50 793 

9.98 001 


45 


16 

9.47 249 

40 

9.49 252 

45 

10.50 748 

9.97 997 

4 

44 


17 

9.47 290 

41 

9.49 296 

44 

10.50 704 

9.97 993 

4 

43 


18 

9.47 330 

40 

9.49 341 

45 

10.50 659 

9.97 989 

4 

42 


19 

9.47 371 

41 

40 

9.49 385 

44 

45 

10.50 615 

9.97 986 

3 

4 

41 


20 

9.47 411 

9.49 430 

10.50 570 

9.97 982 


40 


21 

9.47 452 

41 

9.49 474 

44 

10.50 526 

9.97 978 

4 

39 


22 

9.47 492 

40 

9.49 519 

45 

10.50 481 

9.97 974 

4 

38 


23 

9.47 533 

41 

9.49 563 

44 

10.50 437 

9.97 970 

4 

37 


24 

9.47 573 

40 

40 

9.49 607 

44 

45 

10.50 393 

9.97 966 

4 

A 

36 

] 

25 

9.47 613 

9.49 652 

10.50 348 

9.97 962 


35 


26 

9.47 654 

41 

9.49 696 

44 

10.50 304 

9.97 958 

4 

34 


27 

9.47 694 

40 

9.49 740 

44 

10.50 260 

9.97 954 

4 

33 

I 

28 

9.47 734 

40 

9.49 784 

44 

10.50 216 

9.97 950 

4 

32 


29 

9.47 774 

40 

40 

9.49 828 

44 

44 

10.50 172 

9.97 946 

4 

A 

31 


30 

9.47 814 

9.49 872 

10.50 128 

9.97 942 


30 


31 

9.47 854 

40 

9.49 916 

44 

10.50 084 

9.97 938 

4 

29 


32 

9.47 894 

40 

9.49 960 

44 

10.50 040 

9.97 934 

4 

28 


33 

9.47 934 

40 

9.50 004 

44 

10.49 996 

9.97 930 

4 

27 


34 

9.47 974 

40 

40 

9.50 048 

44 

44 

10.49 952 

9.97 926 

4 

A 

26 


35 

9.48 014 

9.50 092 

10.49 908 

9.97 922 


25 


36 

9.48 054 

40 

9.50 136 

44 

10.49 864 

9.97 918 

4 

24 


37 

9.48 094 

40 

9.50 180 

44 

10.49 820 

9.97 914 

4 

23 


38 

9.48 133 

39 

9.50 223 

43 

10.49 777 

9.97 910 

4 

22 


39 

9.48 173 

40 

40 

9.50 267 

44 

44 

10.49 733 

9.97 906 

4 

A 

21 


40 

9.48 213 

9.50 311 

10.49 689 

9.97 902 


20 


41 

9.48 252 

39 

9.50 355 

44 

10.49 645 

9.97 898 

4 

19 


42 

9.48 292 

40 

9.50 398 

43 

10.49 602 

9.97 894 

4 

18 


43 

9.48 332 

40 

9.50 442 

44 

10.49 558 

9.97 890 

4 

17 


44 

9.48 371 

39 

40 

9.50 485 

43 

44 

10.49 515 

9.97 886 

4 

A 

16 


45 

9.48 411 

9.50 529 

10.49 471 

9.97 882 


15 


46 

9.48 450 

39 

9.50 572 

43 

10.49 428 

9.97 878 

4 

14 


47 

9.48 490 

40 

9.50 616 

44 

10.49 384 

9.97 874 

4 

13 


48 

9.48 529 

39 

9.50 659 

43 

10.49 341 

9.97 870 

4 

12 


49 

9.48 568 

39 

39 

9.50 703 

44 

43 

10.49 297 

9.97 866 

4 

11 


50 

9.48 607 


9.50 746 


10.49 254 

9.97 861 

O 

10 


51 

9.48 647 

40 

9.50 789 

43 

10.49 211 

9.97 857 

4 

9 


52 

9.48 686 

39 

9.50 833 

44 

10.49 167 

9.97 853 

4 

8 

] 

53 

9.48 725 

39 

9.50 876 

43 

10.49 124 

9.97 849 

4 

7 


54 

9.48 764 

39 

9.50 919 

43 

43 

10.49 081 

9.97 845 

4 

6 


55 

9.48 803 

oy 

9.50 962 

10.49 038 

9.97 841 


5 

4 

c 

56 

9.48 842 

39 

9.51 005 

43 

10.48 995 

9.97 837 

4 

4 


57 

9.48 881 

39 

9.51 048 

43 

10.48 952 

9.97 833 

4 

3 


58 

9.48 920 

39 

9.51 092 

44 

10.48 908 

9.97 829 

4 

2 


59 

9.48 959 

39 

9.51 135 

43 

10.48 865 

9.97 825 

4 

1 




39 







60 

9.48 998 

9.51 178 


10.48 822 

9.97 821 


0 



L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

/ 



Prop. Pts. 


45 

44 

4.5 

4.4 

5.3 

5.1 

6.0 

5.9 

6.8 

6.6 

7.5 

7.3 

15.0 

14.7 

22.5 

22.0 

30.0 

29.3 

37.5 

36.7 


43 

4.3 
5.0 
5.7 

6.4 
7.2 

14.3 

21.5 

28.7 

35.8 


42 

4.2 

4.9 

5.6 

6.3 
7.0 

14.0 

21.0 

28.0 

35.0 


4.0 

4.7 

5.3 
6.0 

6.7 

13.3 
20.0 

26.7 

33.3 



5 

4 

6 

0.5 

0.4 

7 

0.6 

0.5 

8 

0.7 

0.5 

9 

0.8 

0.6 

10 

0.8 

0.7 

20 

1.7 

1.3 

30 

2.5 

2.0 

40 

3.3 

2.7 

50 

4.2 

3.3 


41 

4.1 

4.8 

5.5 

6.2 

6.8 

13.7 

20.5 

27.3 
34.2 


39 

3.9 
4.6 
5.2 

5.9 

6.5 

13.0 

19.5 
26.0 

32.5 


Prop. Pts. 


72 ' 


















































































VI 


FIVE-PLACE logarithms OF FUNCTIONS 


45 


18 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.48 998 

39 

9.51 178 


10.48 822 

9.97 821 


60 

1 

9.49 037 

9.51 221 

43 

10.48 779 

9.97 817 

4 

59 

2 

9.49 076 


9.51 264 

43 

10.48 736 

9.97 812 

5 

58 

3 

9.49 115 


9.51 306 

42 

10.48 694 

9.97 808 

4 

57 

4 

9.49 153 

39 

9.51 349 

43 

43 

10.48 651 

9.97 804 

4 

56 

5 

9.49 192 

9.51 392 

10.48 608 

9.97 800 

4 

55 

6 

9.49 231 


9.51 435 

43 

10.48 565 

9.97 796 

4 

54 

7 

9.49 269 


9.51 478 

43 

10.48 522 

9.97 792 

4 

53 

8 

9.49 308 


9.51 520 

42 

10.48 480 

9.97 788 

4 

52 

9 

9.49 347 

3S 

9.51 563 

43 

43 

10.48 437 

9.97 784 

4 

51 

10 

9.49 385 


9.51 606 

10.48 394 

9.97 779 

5 

50 

11 

9.49 424 


9.51 648 

42 

10.48 352 

9.97 775 

4 

49 

12 

9.49 462 


9.51 691 

43 

10.48 309 

9.97 771 

4 

48 

13 

9.49 500 


9.51 734 

43 

10.48 266 

9.97 767 

4 

47 

14 

9.49 539 

38 

9.51 776 

42 

43 

10.48 224 

9.97 763 

4 

46 

lo 

9.49 577 

9.51 819 

10.48 181 

9.97 759 

4 

45 

16 

9.49 615 


9.51 861 

42 

10.48 139 

9.97 754 

5 

44 

17 

9.49 654 


9.51 903 

42 

10.48 097 

9.97 750 

4 

43 

18 

9.49 692 


9.51 946 

43 

10.48 054 

9.97 746 

4 

42 

19 

9.49 730 

38 

9.51 988 

42 

43 

10.48 012 

9.97 742 

4 

41 

20 

9.49 768 

9.52 031 

10.47 969 

9.97 738 

4 

40 

21 

9.49 806 


9.52 073 

42 

10.47 927 

9.97 734 

4 

39 

22 

9.49 844 


9.52 115 

42 

10.47 885 

9.97 729 

5 

38 

23 

9.49 882 


9.52 157 

42 

10.47 843 

9.97 725 

4 

37 

24 

9.49 920 

38 

9.52 200 

43 

42 

10.47 800 

9.97 721 

4 

36 

26 

9.49 958 

9.52 242 

10.47 758 

9.97 717 

4 

35 

26 

9.49 996 

38 

9.52 284 

42 

10.47 716 

9.97 713 

4 

34 

27 

9.50 034 

38 

9.52 326 

42 

10.47 674 

9.97 708 

5 

33 

28 

9.50 072 

38 

9.52 368 

42 

10.47 632 

9.97 704 

4 

32 

29 

9.50 110 

38 

38 

9.52 410 

42 

42 

10.47 590 

9.97 700 

4 

31 

30 

9.50 148 

9.52 452 

10.47 548 

9.97 696 

4 

30 

31 

9.50 185 

37 

9.52 494 

42 

10.47 506 

9.97 691 

5 

29 

32 

9.50 223 

38 

9.52 536 

42 

10.47 464 

9.97 687 

4 

28 

33 

9.50 261 

38 

9.52 578 

42 

10.47 422 

9.97 683 

4 

27 

34 

9.50 298 

37 

38 

9.52 620 

42 

41 

10.47 380 

9.97 679 

4 

26 

35 

9.50 336 

9.52 661 

10.47 339 

9.97 674 

5 

25 

36 

9.50 374 

38 

9.52 703 

42 

10.47 297 

9.97 670 

4 

24 

37 

9.50 411 

37 

9.52 745 

42 

10.47 255 

9.97 666 

4 

23 

38 

9.50 449 

38 

9.52 787 

42 

10.47 213 

9.97 662 

4 

22 

39 

9.50 486 

37 

37 

9.52 829 

42 

41 

10.47 171 

9.97 657 

5 

21 

40 

9.50 523 

9.52 870 

10.47 130 

9.97 653 


20 

41 

9.50 561 

38 

9.52 912 

42 

10.47 088 

9.97 649 

4 

19 

42 

9.50 598 

37 

9.52 953 

41 

10.47 047 

9.97 645 

4 

18 

43 

9.50 635 

37 

9.52 995 

42 

10.47 005 

9.97 640 

5 

17 

44 

9.50 673 

38 

37 

9.53 037 

42 

41 

10.46 963 

9.97 636 

4 

16 

45 

9.50 710 

9.53 078 

10.46 922 

9.97 632 


15 

46 

9.50 747 

37 

9.53 120 

42 

10.46 880 

9.97 628 

4 

14 

47 

9.50 784 

37 

9.53 161 

41 

10.46 839 

9.97 623 

5 

13 

48 

9.50 821 

37 

9.53 202 

41 

10.46 798 

9.97 619 

4 

12 

49 

9.50 858 

37 

38 

9.53 244 

42 

41 

10.46 756 

9.97 615 

4 

11 

60 

9.50 896 

9.53 285 

10.46 715 

9.97 610 


10 

51 

9.50 933 

37 

9.53 327 

42 

10.46 673 

9.97 606 

4 

9 

52 

9.50 970 

37 

9.53 368 

41 

10.46 632 

9.97 602 

4 

8 

53 

9.51 007 

37 

9.53 409 

41 

10.46 591 

9.97 597 

5 

7 

54 

9.51 043 

36 

9.53 450 

41 

10.46 550 

9.97 593 

4 

6 



37 


42 





55 

9.51 080 

9.53 492 

10.46 508 

9.97 589 


5 

56 

9.51 117 

37 

9.53 533 

41 

10.46 467 

9.97 584 

5 

4 

57 

9.51 154 

37 

9.53 574 

41 

10.46 426 

9.97 580 

4 

3 

58 

9.51 191 

37 

9.53 615 

41 

10.46 385 

9.97 576 

4 

2 

59 

9.51 227 

36 

37 

9.53 656 

41 

41 

10.46 344 

9.97 571 

5 

1 

60 

9.51 264 

9.53 697 

10.46 303 

9.97 567 


0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 


Prop. Pts. 



43 

42 

41 

6 

4.3 

4.2 

4.1 

7 

5.0 

4.9 

4.8 

8 

5.7 

5.6 

5.5 

9 

6.4 

6.3 

6.2 

10 

7.2 

7.0 

6.8 

20 

14.3 

14.0 

13.7 

30 

21.5 

21.0 

20.5 

40 

28.7 

28.0 

27.3 

50 

35.8 

35.0 

34.2 


" 

39 

38 

37 

6 

3.9 

3.8 

3.7 

7 

4.6 

4.4 

4.3 

8 

5.2 

5.1 

4.9 

9 

5.9 

5.7 

5.6 

10 

6.5 

6.3 

6.2 

20 

13.0 

12.7 

12.3 

30 

19.5 

19.0 

18.5 

40 

26.0 

25.3 

24.7 

50 

32.5 

31.7 

30.8 


" 

36 

5 

4 

6 

3.6 

0.5 

0.4 

7 

4.2 

0.6 

0.5 

8 

4.8 

0.7 

0.5 

9 

5.4 

0.8 

0.6 

10 

6.0 

0.8 

0.7 

20 

12.0 

1.7 

1.3 

30 

18.0 

2.5 

2.0 

40 

24.0 

3.3 

2.7 

50 

30.0 

4.2 

3.3 


Prop. Pts. 


7r 





































































46 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


19 ° 


/ 

L Sin 

d 

L Tan 

1 c d 

1 L Cot 

L Cos 

d 


Prop. Pts. 

0 

9.51 264 


9.5.3 697 


1 10.46 303 

9.97 567 


60 





1 

9.51 301 

37 

9.53 738 

41 

! 10.46 262 

9.97 563 

4 

59 





2 

9.51 338 

37 

9.53 779 

41 

1 10.46 221 

9.97 558 

5 

58 





3 

9.51 374 

36 

9.53 820 

41 

! 10.46 180 

9.97 554 

4 

57 





4 

9.51 411 

37 

36 

9.53 861 

41 

41 

10.46 139 

9.97 550 

4 

56 





5 

9.51 447 

9.53 902 

10.46 098 

9.97 545 


55 





6 

9.51 484 

37 

9.53 943 

41 

10.46 057 

9.97 541 

4 

54 





7 

9.51 520 

36 

9.53 984 

41 

10.46 016 

9.97 536 

5 

53 

„ 

41 

40 

39 

8 

9.51 557 

37 

9.54 025 

41 

10.45 975 

9.97 532 

4 

52 





9 

9.51 593 

36 

9.54 065 

40 

10.45 935 

9.97 528 

4 

51 

6 

1 4.1 

4.C 

> 3.9 



36 


41 







; 4.7 
1 5 3 


10 

9.51 629 

9.54 106 

10.45 894 

9.97 523 


50 

7 

g 

4.8 
5 5 

4.6 

; 5 2 

11 

9.51 666 

37 

9.54 147 

41 

10.45 853 

9.97 519 

4 

49 

9 

6!2 

6!o 

1 5^9 

12 

9.51 702 

36 

9.54 187 

■ 40 

10.45 813 

9.97 515 

4 

48 

10 

' 6.8 

6.7 

6.5 

13 

9.51 738 

36 

9.54 228 


10.45 772 

9.97 510 

5 

47 

20 

13.7 

13.3 

13.0 

14 

9.51 774 

36 

9.54 269 

41 

10.45 731 

9.97 506 

4 

46 

30 

20.5 

20.0 

19.5 



37 







40 

27 3 

26 7 

26 0 

15 

9.51 811 

9.54 309 


10.45 691 

9.97 501 


45 

50 

34]2 

33.3 

32.5 

16 

9.51 847 

36 

9.54 350 

41 

10.45 650 

9.97 497 

4 

44 





17 

9.51 883 

36 

9.54 390 

40 

10.45 610 

9.97 492 

5 

43 





18 

9.51 919 

36 

9.54 431 

41 

10.45 569 

9.97 488 

4 

42 





19 

9.51 955 

36 

36 

9.54 471 

40 

41 

10.45 529 

9.97 484 

4 

41 





20 

9.51 991 

9.54 512 

10.45 488 

9.97 479 

O 

40 





21 

9.52 027 

36 

9..54 552 

40 

10.45 448 

9.97 475 

4 

39 





22 

9.52 063 

36 

9.54 593 

41 

10.45 407 

9.97 470 

5 

38 





23 

9.52 099 

36 

9.54 633 

40 

10.45 367 

9.97 466 

4 

37 





24 

9.52 135 

36 

36 

9.54 673 

40 

41 

10.45 327 

9.97 461 

5 

A 

36 





25 

9.52 171 

9.54 714 


10.45 286 

9.97 457 


35 





26 

9.52 207 

36 

9.54 754 

40 

10.45 246 

9.97 453 

4 

34 

n 

37 

36 

35 

27 

9.52 242 

35 

9.54 794 

40 

10.45 206 

9.97 448 

5 

33 





28 

9.52 278 

36 

9.54 835 ! 

41 

10.45 165 

9.97 444 

4 

32 

6 

3.7 

3.6 

3.5 

29 

9.52 314 

36 

36 

9.54 875 

40 

40 

10.45 125 

9.97 439 

5 

A 

31 

7 

8 

4.3 
4 9 

4.2 
4 8 

4.1 

4 7 

30 

9.52 350 

9.54 915 

10.45 085 

9.97 435 


30 

9 

5.6 

5.4 

5.3 

31 

9.52 385 

35 

9.54 955 

40 

10.45 045 

9.97 430 

5 

29 

10 

6.2 

6.0 

5.8 

32 

9.52 421 

36 

9.54 995 

40 

10.45 005 

9.97 426 

4 

28 

20 

12.3 

12.0 

11.7 

33 

9.52 456 

35 

9.55 035 

40 

10.44 965 

9.97 421 

5 

27 

30 

18.5 

94. 7 

18.0 
9J. n 

17.5 

34 

9.52 492 

36 

35 

9.55 075 

40 

40 

10.44 925 

9.97 417 

4 

26 

^\J 

50 

30.8 

30.0 

^0.0 

29.2 

35 

9.52 527 


9.55 115 

10.44 885 

9.97 412 


25 





36 

9.52 563 

36 

9.55 155 

40 

10.44 845 

9.97 408 

4 

24 





37 

9.52 598 

35 

9.55 195 

40 

10.44 805 

9.97 403 

5 

23 





38 

9.52 634 

36 

9.55 235 

40 

10.44 765 

9.97 399 

4 

22 





39 

9.52 669 

35 

36 

9.55 275 

40 

40 

10.44 725 

9.97 394 

5 

21 





40 

9.52 705 

9.55 315 

10.44 685 

9.97 390 


20 





41 

9.52 740 

35 

9.55 355 

40 

10.44 645 

9.97 385 

5 

19 





42 

9.52 775 

35 

9.55 395 

40 

10.44 605 

9.97 381 

4 

18 





43 

9.52 811 

36 

9.55 4.34 

39 

10.44 566 

9.97 376 

5 

17 





44 

9.52 846 

35 

35 

9.55 474 

40 

40 

10.44 526 

9.97 372 

4 

16 





45 

9.52 881 

9.55 514 

10.44 486 

9.97 367 

0 

15 

// 

34 

5 

4 

46 

9.52 916 

35 

9.55 554 

40 

10.44 446 

9.97 363 

4 

14 





47 

9.52 951 

35 

9.55 593 

39 

10.44 407 

9.97 358 

5 

13 

6 

3.4 

0.5 

0.4 

48 

9.52 986 

35 

9.55 633 

40 

10.44 367 

9.97 353 

5 

12 

7 

Q 

4.0 

4 K 

0.6 
O 7 

0.5 

o 

49 

9.53 021 

35 

35 

9.55 673 

40 

39 

10.44 327 

9.97 349 

4 

11 

o 

9 

*±.o 

5.1 

U. 1 
0.8 

u.o 

0.6 

60 

9.53 056 

9.55 712 

10.44 288 

9.97 344 


10 

10 

5.7 

0.8 

0.7 

51 

9.53 092 

36 

9.55 752 

40 

10.44 248 

9.97 340 

4 

9 

20 

•in 

11.3 

17 0 

1.7 

9 

1.3 

9 O 

52 

9.53 126 

34 

9.55 791 

39 

10.44 209 

9.97 335 

5 

8 

oU 

40 

1 / .U 

22.7 

3.3 

Z.U 

2.7 

53 

9.53 161 

35 

9.55 831 

40 

10.44 169 

9.97 331 

4 

7 

50 

28.3 

4.2 

3.3 

54 

9.53 196 

35 

35 

9.55 870 

39 

An 

10.44 130 

9.97 326 

5 

A 

6 





55 

9.53 231 

9.55 910 


10.44 090 

9.97 322 


5 





56 

9.53 266 

35 

9.55 949 

39 

10.44 051 

9.97 317 

5 

4 





57 

9.53 301 

35 

9.55 989 

40 

10.44 on 

9.97 312 

5 

3 





58 

9.53 336 

35 

9.56 028 

39 

10.43 972 

9.97 308 

4 

2 





59 

9.53 370 

34 

35 

9.56 067 

39 

40 

10.43 933 

9.97 303 

5 

1 





60 

9.53 405 

9.56 107 

10.43 893 

9.97 299 








L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

/ 

Prop. Pts. 


70 ' 


















































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


47 


20 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.53 405 


9.56 107 


10.43 893 

9.97 299 


60 

1 

9.53 440 

35 

9.56 146 

39 

10.43 854 

9.97 294 

5 

59 

2 

9.53 475 

55 

9.56 185 

39 

10.43 815 

9.97 289 

5 

58 

3 

9.53 509 

34 

9.56 224 

39 

10.43 776 

9.97 285 

4 

57 

4 

9.53 544 

55 

34 

9.56 264 

40 

39 

10.43 736 

9.97 280 

5 

4 

56 

5 

9.53 578 

9.56 303 

10.43 697 

9.97 276 


55 

6 

9.53 613 

35 

9.56 342 

39 

10.43 658 

9.97 271 

5 

54 

7 

9.53 647 

34 

9.56 381 

39 

10.43 619 

9.97 266 

5 

53 

8 

9.53 682 

35 

9.56 420 

39 

10.43 580 

9.97 262 

4 

52 

9 

9.53 716 

34 

35 

9.56 459 

39 

39 

10.43 541 

9.97 257 

5 

5 

51 

10 

9.53 751 

9.56 498 

10.43 502 

9.97 252 


50 

11 

9.53 785 

34 

9.56 537 

39 

10.43 463 

9.97 248 

4 

49 

12 

9.53 819 

34 

9.56 576 

39 

10.43 424 

9.97 243 

5 

48 

13 

9.53 854 

55 

9.56 615 

39 

10.43 385 

9.97 238 

5 

47 

14 

9.53 888 

34 

9.56 654 

39 

39 

10.43 346 

9 97 234 

4 

5 

46 

15 

9.53 922 


9.56 693 

10.43 307 

9.97 229 


45 

16 

9.53 957 

55 

9.56 732 

39 

10.43 268 

9.97 224 

5 

44 

17 

9.53 991 

34 

9.56 771 

39 

10.43 229 

9.97 220 

4 

43 

18 

9.54 025 

34 

9.56 810 

39 

10.43 190 

9.97 215 

5 

42 

19 

9.54 059 

34 

9.56 849 

39 

10.43 151 

9.97 210 

5 

4 

41 

20 

9.54 093 


9.56 887 


10.43 113 

9.97 206 


40 

21 

9.54 127 

34 

9.56 926 

39 

10.43 074 

9.97 201 

5 

39 

22 

9.54 161 

34 

9.56 965 

39 

10.43 035 

9.97 196 

5 

38 

23 

9.54 195 

34 

9.57 004 

39 

10.42 996 

9.97 192 

4 

37 

24 

9.54 229 

34 

9.57 042 

38 

10.42 958 

9.97 187 

5 

5 

36 

25 

9.54 263 


9.57 081 


10.42 919 

9.97 182 


35 

26 

9.54 297 

34 

9.57 120 

39 

10.42 880 

9.97 178 

4 

34 

27 

9.54 331 

34 

9.57 158 

38 

10.42 842 

9.97 173 

5 

33 

28 

9.54 365 

34 

9.57 197 

39 

10.42 803 

9.97 168 

5 

32 

29 

9.54 399 

34 

Q A 

9.57 235 

38 

10.42 765 

9.97 163 

5 

4 

31 

30 

9.54 433 


9.57 274 

O t7 

10.42 726 

9.97 159 


30 

31 

9.54 466 

33 

9.57 312 

38 

10.42 688 

9.97 154 

5 

29 

32 

9.54 500 

34 

9.57 351 

39 

10.42 649 

9.97 149 

5 

28 

33 

9.54 534 

34 

9.57 389 

38 

10.42 611 

9.97 145 

4 

27 

34 

9.54 567 

33 

Q A 

9.57 428 

39 

10.42 572 

9.97 140 

5 

5 

26 

35 

9.54 601 

54 

9.57 466 

oo 

10.42 534 

9.97 135 


25 

36 

9.54 635 

34 

9.57 504 

38 

10.42 496 

9.97 130 

5 

24 

37 

9.54 668 

33 

9.57 543 

39 

10.42 457 

9.97 126 

4 

23 

38 

9.54 702 

34 

9.57 581 

38 

10.42 419 

9.97 121 

5 

22 

39 

9.54 735 

33 

Q A 

9.57 619 

38 

39 

10.42 381 

9.97 116 

5 

5 

21 

40 

9.54 769 

54 

9.57 658 


10.42 342 

9.97 111 


20 

41 

9.54 802 

33 

9.57 696 

38 

10.42 304 

9.97 107 

4 

19 

42 

9.54 836 

34 

9.57 734 

38 

10.42 266 

9.97 102 

5 

18 

43 

9.54 869 

33 

9.57 772 

38 

10.42 228 

9.97 097 

5 

17 

44 

9.54 903 

34 

9.57 810 

38 

QQ 

10.42 190 

9.97 092 

5 

5 

16 

45 

9.54 936 

33 

9.57 849 

oy 

10.42 151 

9.97 087 

A 

15 

46 

9.54 969 

33 

9.57 887 

38 

10.42 113 

9.97 083 


14 

47 

9.55 003 

34 

9.57 925 

38 

10.42 075 

9.97 078 

5 

13 

48 

9.55 036 

33 

9.57 963 

38 

10.42 037 

9.97 073 

5 

12 

49 

9.55 069 

33 

9.58 001 

38 

38 

10.41 999 

9.97 068 

5 

5 

11 

50 

9.55 102 

33 

9.58 039 


10.41 961 

9.97 063 

A 

10 

51 

9.55 136 

34 

9.58 077 

38 

10.41 923 

9.97 059 

4 

r 

9 

52 

9.55 169 

33 

9.58 115 

38 

10.41 885 

9.97 054 

0 

r 

8 

53 

9.55 202 

33 

9.58 153 

38 

10.41 847 

9.97 049 

O 

7 

54 

9.55 235 

33 

9.58 191 

38 

10.41 809 

9.97 044 

0 

5 

6 

55 

9.55 268 

33 

9.58 229 

oo 

10.41 771 

9.97 039 

A 

5 

56 

9.55 301 

33 

9.58 267 

38 

10.41 733 

9.97 035 

fr 

4 

57 

9.55 334 

33 

9.58 304 

37 

10.41 696 

9.97 030 

O 

3 

58 

9.55 367 

33 

9.58 342 

38 

10.41 658 

9.97 025 

O 

2 

59 

9.55 400 

33 

9.58 380 

38 

10.41 620 

9.97 020 

0 

5 

1 

60 

9.55 433 

33 

9.58 418 

Oo 

10.41 582 

9.97 015 


0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 


Prop. Pts. 


40 

4.0 

4.7 
5.3 
6.0 

6.7 

13.3 
20.0 
26.7 

33.3 


3.8 

4.4 

5.1 

5.7 

6.3 

12.7 
19.0 
25.3 

31.7 


35 

3.5 

4.1 

4.7 
5.3 

5.8 
11.7 
17.5 
23.3 
29.2 


39 

3.9 
4.6 
5.2 

5.9 
6.5 

13.0 

19.5 
26.0 

32.5 


37 

3.7 

4.3 

4.9 

5.6 

6.2 

12.3 

18.5 

24.7 


34 

3.4 
4.0 

4.5 
5.1 
5.7 

11.3 
17.0 
22.7 

28.3 


3.3 
3.8 

4.4 
5.0 

5.5 
11.0 
16.5 


22.0 3.3 
27.514.2 


Prop. Pts. 


69 ' 














































































48 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


2r 


r 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.55 433 


9.58 418 


10.41 582 

9.97 015 


60 

1 

9.55 466 

33 

9.58 455 

37 

10.41 545 

9.97 010 

5 

59 

2 

9.55 499 

33 

9.58 493 

38 

10.41 507 

9.97 005 

5 

58 

3 

9.55 532 

33 

9.58 531 

38 

10.41 469 

9.97 001 

4 

57 

4 

9.55 564 

32 

9.58 569 

38 

10.41 431 

9.96 996 

5 

56 





37 





5 

9.55 597 


9.58 606 

10.41 394 

9.96 991 


55 

6 

9.55 630 

33 

9.58 644 

38 

10.41 356 

9.96 986 

5 

54 

7 

9.55 663 

33 

9.58 681 

37 

10.41 319 

9.96 981 

5 

53 

8 

9.55 695 

32 

9.58 719 

38 

10.41 281 

9.96 876 

5 

52 

9 

9.55 728 

33 

9.58 757 

38 

37 

10.41 243 

9.96 971 

5 

51 

10 

9.55 761 


9.58 794 

10.41 206 

9.96 966 

o 

50 

11 

9.55 793 

32 

9.58 832 

38 

10.41 168 

9.96 962 

4 

49 

12 

9.55 826 

33 

9.58 869 

37 

10.41 131 

9.96 957 

5 

48 

13 

9.55 858 

32 

9.58 907 

38 

10.41 093 

9.96 952 

5 

47 

14 

9.55 891 

33 

32 

9.58 944 

37 

37 

10.41 056 

9.96 947 

5 

46 

15 

9.55 923 

9.58 981 

10.41 019 

9.96 942 

O 

45 

16 

9.55 956 

33 

9.59 019 

38 

10.40 981 

9.96 937 

5 

44 

17 

9.55 988 

32 

9.59 056 

37 

10.40 944 

9.96 932 

5 

43 

18 

9.56 021 

33 

9.59 094 

38 

10.40 906 

9.96 927 

5 

42 

19 

9.56 053 

32 

32 

9.59 131 

37 

37 

10.40 869 

9.96 922 

5 

41 

20 

9.56 085 

9.59 168 

10.40 832 

9.96 917 


40 

21 

9.56 118 

33 

9.59 205 

37 

10.40 795 

9.96 912 

5 

39 

22 

9.56 150 

32 

9.59 243 

38 

10.40 757 

9.96 907 

5 

38 

23 

9.56 182 

32 

9.59 280 

37 

10.40 720 

9.96 903 

4 

37 

24 

9.56 215 

33 

32 

9.59 317 

37 

37 

10.40 683 

9.96 898 

5 

36 

25 

9.56 247 

9.59 354 

10.40 646 

9.96 893 

O 

35 

26 

9.56 279 

32 

9.59 391 

37 

10.40 609 

9.96 888 

5 

34 

27 

9.56 311 

32 

9.59 429 

38 

10.40 571 

9.96 883 

5 

33 

28 

9.56 343 

32 

9.59 466 

37 

10.40 534 

9.96 878 

5 

32 

29 

9.56 375 

32 

33 

9.59 503 

37 

37 

10.40 497 

9.96 873 

5 

31 

30 

9.56 408 

9.59 540 

10.40 460 

9.96 868 

o 

30 

31 

9.56 440 

32 

9.59 577 

37 

10.40 423 

9.96 863 

5 

29 

32 

9.56 472 

32 

9.59 614 

37 

10.40 386 

9.96 858 

5 

28 

33 

9.56 504 

32 

9.59 651 

37 

10.40 349 

9.96 853 

5 

27 

34 

9.56 536 

32 

32 

9.59 688 

37 

37 

10.40 312 

9.96 848 

5 

26 

35 

9.56 568 

9.59 725 

10.40 275 

9.96 843 

0 

25 

36 

9.56 599 

31 

9.59 762 

37 

10.40 238 

9.96 838 

5 

24 

37 

9.56 631 

32 

9.59 799 

37 

10.40 201 

9.96 833 

5 

23 

38 

9.56 663 

32 

9.59 835 

36 

10.40 165 

9.96 828 

5 

22 

39 

9.56 695 

32 

9.59 872 

37 

10.40 128 

9.96 823 

5 

21 



32 


37 





40 

9.56 727 

9.59 909 

10.40 091 

9.96 818 

0 

20 

41 

9.56 759 

32 

9.59 946 

37 

10.40 054 

9.96 813 

5 

19 

42 

9.56 790 

31 

9.59 983 

37 

10.40 017 

9.96 808 

5 

18 

43 

9.56 822 

32 

9.60 019 

36 

10.39 981 

9.96 803 

5 

17 

44 

9.56 854 

32 

32 

9.60 056 

37 

37 

10.39 944 

9.96 798 

5 

r 

16 

45 

9.56 886 

9.60 093 

10.39 907 

9.96 793 

O 

15 

46 

9.56 917 

31 

9.60 130 

37 

10.39 870 

9.96 788 

5 

14 

47 

9.56 949 

32 

9.60 166 

36 

10.39 834 

9.96 783 

5 

13 

48 

9.56 980 

31 

9.60 203 

37 

10.39 797 

9.96 778 

5 

12 

49 

9.57 012 

32 

32 

9.60 240 

37 

36 

10.39 760 

9.96 772 

6 

11 

50 

9.57 044 

9.60 276 

10.39 724 

9.96 767 

0 

10 

51 

9.57 075 

31 

9.60 313 

37 

10.39 687 

9.96 762 

5 

9 

52 

9.57 107 

32 

9.60 349 

36 

10.39 651 

9.96 757 

5 

8 

53 

9.57 138 

31 

9.60 386 

37 

10.39 614 

9.96 752 

5 

7 

54 

9.57 169 

31 

9.60 422 

36 

10.39 578 

9.96 747 

5 

6 



32 


37 





55 

9.57 201 

9.60 459 

10.39 541 

9.96 742 


5 

56 

9.57 232 

31 

9.60 495 

36 

10.39 505 

9.96 737 

5 

4 

57 

9.57 264 

32 

9.60 532 

37 

10.39 468 

9.96 732 

5 

3 

58 

9.57 295 

31 

9.60 568 

36 

10.39 432 

9.96 727 

5 

2 

59 

9.57 326 

31 

32 

9.60 605 

37 

36 

10.39 395 

9.96 722 

5 

c 

1 

60 

9.57 358 

9.60 641 

10.39 359 

9.96 717 

O 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

/ 


Prop. Pts. 


" 

38 

37 

6 

•3.8 

3.7 

7 

4.4 

4.3 

8 

5.1 

4.9 

9 

5.7 

5.6 

10 

6.3 

6.2 

20 

12.7 

12.3 

30 

19.0 

18.5 

40 

25.3 

24.7 

50 

31.7 

30.8 


36 

3.6 

4.2 

4.8 

5.4 

6.0 

12.0 

18.0 

24.0 

30.0 


" 

33 

32 

31 

6 

3.3 

3.2 

3.1 

7 

3.9 

3.7 

3.6 

8 

4.4 

4.3 

4.1 

9 

5.0 

4.8 

4.6 

10 

5.5 

5.3 

5.2 

20 

11.0 

10.7 

10.3 

30 

16.5 

16.0 

15.5 

40 

22.0 

21.3 

20.7 

50 

27.5 

26.7 

25.8 



6 

5 

6 

0.6 

0.5 

7 

0.7 

0.6 

8 

0.8 

0.7 

9 

0.9 

0.8 

10 

1.0 

0.8 

20 

2.0 

1.7 

30 

3.0 

2.5 

40 

4.0 

3.3 

50 

5.0 

4.2 


Prop. Pts. 


68 ' 










































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


49 


22 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 



0 

9.57 358 


9.60 641 


10.39 359 

9.96 717 


60 


1 

9.57 389 

31 

9.60 677 

36 

10.39 323 

9.96 711 

6 

59 


2 

9.57 420 

31 

9.60 714 

37 

10.39 286 

9.96 706 

5 

58 


3 

9.57 451 

31 

9.60 750 

36 

10.39 250 

9.96 701 

5 

57 


4 

9.57 482 

31 

32 

9.60 786 

36 

37 

10.39 214 

9.96 696 

5 

c 

56 


5 

9.57 514 

9.60 823 

10.39 177 

9.96 691 

O 

55 


6 

9.57 545 

31 

9.60 859 

36 

10.39 141 

9.96 686 

5 

54 


7 

9.57 576 

31 

9.60 895 

36 

10.39 105 

9.96 681 

5 

53 

,, 

8 

9.57 607 

31 

9.60 931 

36 

10.39 069 

9.96 676 

5 

52 


9 

9.57 638. 

31 

31 

9.60 967 

36 

37 

10.39 033 

9.96 670 

6 

51 

6 

10 

9.57 669 

9.61 004 

10.38 996 

9.96 665 

o 

50 

7 

8 

11 

9.57 700 

31 

9.61 040 

36 

10.38 960 

9.96 660 

5 

49 

9 

12 

9.57 731 

31 

9.61 076 

36 

10.38 924 

9.96 655 

5 

48 

10 

13 

9.57 762 

31 

9.61 112 

36 

10.38 888 

9.96 650 

5 

47 

20 

14 

9.57 793 

31 

31 

9.61 148 

36 

36 

10.38 852 

9.96 645 

' 5 

46 

30 

40 

15 

9.57 824 

9.61 184 

10.38 816 

9.96 640 

O 

45 

50 

16 

9.57 855 

31 

9.61 220 

36 

10.38 780 

9.96 634 

6 

44 


17 

9.57 885 

30 

9.61 256 

36 

10.38 744 

9.96 629 

5 

43 


18 

9.57 916 

31 

9.61 292 

36 

10.38 708 

9.96 624 

5 

42 


19 

9.57 947 

31 

31 

9.61 328 

36 

10.38 672 

9.96 619 

5 

41 


20 

9.57 978 

9.61 364 


10.38 636 

9.96 614 

O 

40 


21 

9.58 008 

30 

9.61 400 

36 

10.38 600 

9.96 608 

6 

39 


22 

9.58 039 

31 

9.61 436 

36 

10.38 564 

9.96 603 

5 

38 


23 

9.58 070 

31 

9.61 472 

36 

10.38 528 

9.96 598 

5 

37 


24 

9.58 101 

31 

30 

9.61 508 

36 

10.38 492 

9.96 593 

5 

36 


25 

9.58 131 

9.61 544 


10.38 456 

9.96 588 

o 

35 


26 

9.58 162 

31 

9.61 579 

35 

10.38 421 

9.96 582 

6 

34 


27 

9.58 192 

30 

9.61 615 

36 

10.38 385 

9.96 577 

5 

33 


28 

9.58 223 

31 

9.61 651 

36 

10.38 349 

9.96 572 

5 

32 

6 

29 

9.58 253 

30 

31 

9.61 687 

36 

Q K 

10.38 313 

9.96 567 

5 

5 

31 

7 

8 

30 

9.58 284 

9.61 722 

OO 

10.38 278 

9.96 562 


30 

9 

31 

9.58 314 

30 

9.61 758 

36 

10.38 242 

9.96 556 

6 

29 

10 

32 

9.58 345 

31 

9.61 794 

36 

10.38 206 

9.96 551 

5 

28 

20 

33 

9.58 375 

30 

9.61 830 

36 

10.38 170 

9.96 546 

5 

27 

oU 

40 

34 

9.58 406 

31 

30 

9.61 865 

3 5 
36 

10.38 135 

9.96 541 

5 

0 

26 

50: 

35 

9.58 436 

9.61 901 

10.38 099 

9.96 535 


25 


36 

9.58 467 

31 

9.61 936 

35 

10.38 064 

9.96 530 

5 

24 


37 

9.58 497 

30 

9.61 972 

36 

10.38 028 

9.96 525 

5 

23 


38 

9.58 527 

30 

9.62 008 

36 

10.37 992 

9.96 520 

5 

22 


39 

9.58 557 

30 

Q 1 

9.62 043 

35 

36 

10.37 957 

9.96 514 

6 

5 

21 


40 

9.58 588 

o i 

9.62 079 

10.37 921 

9.96 509 


20 


41 

9.58 618 

30 

9.62 114 

35 

10.37 886 

9.96 504 

5 

19 


42 

9.58 648 

30 

9.62 150 

36 

10.37 850 

9.96 498 

6 

18 


43 

9.58 678 

30 

9.62 185 

3 5 

10.37 815 

9.96 493 

5 

17 


44 

9.58 709 

31 

9.62 221 

36 

10.37 779 

9.96 488 

5 

5 

16 


45 

9.58 739 

oU 

9.62 256 

oO 

10.37 744 

9.96 483 


15 


46 

9.58 769 

30 

9.62 292 

36 

10.37 708 

9.96 477 

6 

14 

e. 

47 

9.58 799 

30 

9.62 327 

35 

10.37 673 

9.96 472 

5 

13 

C 

7 

48 

9.58 829 

30 

9.62 362 

35 

10.37 638 

9.96 467 

5 

12 

8 

49 

9.58 859 

30 

9.62 398 

36 

10.37 602 

9.96 461 

6 

5 

11 

9 

1C 

20 

50 

9.58 889 

OU 

9.62 433 

OO 

10.37 567 

9.96 456 


10 

51 

9.58 919 

30 

9.62 468 

35 

10.37 532 

9.96 451 

5 

9 

30 

52 

9.58 949 

30 

9.62 504 

36 

10.37 496 

9.96 445 

6 

8 

40 

53 

9.58 979 

30 

9.62 539 

35 

10.37 461 

9.96 440 

5 

7 

50 

54 

9.59 009 

30 

9.62 574 

35 

Q 

10.37 426 

9.96 435 

5 

0 

6 


55 

9.59 039 

OU 

9.62 609 

OO 

10.37 391 

9.96 429 


5 


56 

9.59 069 

30 

9.62 645 

36 

10.37 355 

9.96 424 

5 

4 


57 

9.59 098 

29 

9.62 680 

35 

10.37 320 

9.96 419 

5 

3 


58 

9.59 128 

30 

9.62 715 

35 

10.37 285 

9.96 413 

6 

2 


59 

9.59 158 

30 

9.62 750 

35 

10.37 250 

9.96 408 

5 

5 

1 


60 

9.59 188 

30 

9.62 785 

00 

10.37 215 

9.96 403 


0 



L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 



Prop. Pts. 


37 

36 

3.7 

3.6 

4.3 

4.2 

4.9 

4.8 

5.6 

5.4 

6.2 

6.0 

12.3 

12.0 

18.5 

18.0 

24.7 

24.0 

30.8 

30.0 


35 

3.5 

4.1 

4.7 

5.2 

5.8 
11.7 
17.5 
23.3 
29.2 


32 

31 

30 

3.2 

3.1 

3.0 

3.7 

3.6 

3.5 

4.3 

4.1 

4.0 

4.8 

4.6 

4.5 

5.3 

5.2 

5.0 

10.7 

10.3 

10.0 

16.0 

15.5 

15.0 

21.3 

20.7 

20.0 

26.7 

25.8 

25.0 


29 

6 

2.9 

0.6 

3.4 

0.7 

3.9 

0.8 

4.4 

0.9 

4.8 

1.0 

9.7 

2.0 

14.5 

3.0 

19.3 

4.0 

24.2 

5.0 


Prop. Pts. 


67 ' 









































































50 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


23 ° 


/ 

L Sin 

d 

L X3.n 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

9.59 188 


9.62 785 


10.37 215 

9.96 403 


60 







1 

9.59 218 

30 

9.62 820 

35 

10.37 180 

9.96 397 

6 

59 







2 

9.59 247 

29 

9.62 855 

55 

10.37 145 

9.96 392 

5 

58 







3 

9.59 277 

30 

9.62 890 

35 

10.37 110 

9.96 387 

5 

57 







4 

9.59 307 

30 

29 

9.62 926 

36 

10.37 074 

9.96 381 

6 

56 







5 

9.59 336 

9.62 961 

oO 

10.37 039 

9.96 376 

O 

55 







6 

9.59 366 

30 

9.62 996 

35 

10.37 004 

9.96 370 

6 

54 







7 

9.59 396 

30 

9.63 031 

35 

10.36 969 

9.96 365 

5 

53 

,, 



34 

8 

9.59 425 

29 

9.63 066 

35 

10.36 934 

9.96 360 

5 

52 







9 

9.59 455 

30 

29 

9.63 101 

35 

34 

10.36 899 

9.96 354 

6 

51 

6 

3 

.6 


3.5 

3.4 

10 

9.59 484 

9.63 135 

10.36 865 

9.96 349 

O 

60 

7 

g 

4 8 


4.1 

4.7 

4.0 

4.5 

11 

9.59 514 

30 

9.63 170 

35 

10.36 830 

9.96 343 

6 

49 

9 

5^4 


5.2 

5!i 

12 

9.59 543 

29 

9.63 205 

35 

10.36 795 

9.96 338 

5 

48 

10 

6.0 


5.8 

5.7 

13 

9.59 573 

30 

9.63 240 

35 

10.36 760 

9.96 333 

5 

47 

20 

12.0 

11.7 

11.3 

14 

9.59 602 

29 

30 

9.63 275 

35 

35 

10.36 725 

9.96 327 

6 

c 

46 

30 

40 

18.0 
24 0 

17.5 
23 3 

17.0 

22 7 

15 

9.59 632 

9.63 310 

10.36 690 

9.96 322 

O 

45 

50 

.30.0 

29.2 

28.3 

16 

9.59 661 

29 

9.63 345 

35 

10.36 655 

9.96 316 

6 

44 







17 

9.59 690 

29 

9.63 379 

34 

10.36 621 

9.96 311 

5 

43 







18 

9.59 720 

30 

9.63 414 

35 

10.36 586 

9.96 305 

6 

42 







19 

9.59 749 

29 

29 

9.63 449 

35 

35 

10.36 551 

9.96 300 

5 

a 

41 







20 

9.59 778 

9.63 484 

10.36 516 

9.96 294 

O 

40 







21 

9.59 80-S 

30 

9.63 519 

35 

10.36 481 

9.96 289 

5 

39 







22 

9.59 837 

29 

9.63 553 

34 

10.36 447 

9.96 284 

5 

38 







23 

9.59 866 

29 

9.63 588 

35 

10.36 412 

9.96 278 

6 

37 







24 

9.59 895 

29 

9.63 623 

35 

10.36 377 

9.96 273 

5 

36 









29 


34 











25 

9.59 924 

9.63 657 

10.36 343 

9.96 267 


35 







26 

9.59 954 

30 

9.63 692 

3 5 

10.36 308 

9.96 262 

5 

34 

// 

3( 

) 

S 

S9 

28 

27 

9.59 983 

29 

9.63 726 

34 

10.36 274 

9.96 256 

6 

33 







28 

9.60 012 

29 

9.63 761 

35 

10.36 239 

9.96 251 

5 

32 

6 

3.0 

2.9 

2.8 

29 

9.60 041 

29 

29 

9.63 796 

35 

34 

10.36 204 

9.96 245 

6 

31 

7 

8 

3.5 
4 0 

3.4 
3 9 

3.3 

3 7 

30 

9.60 070 

9.63 830 

10.36 170 

9.96 240 


30 

9 

4.5 

4.4 

4.2 

31 

9.60 099 

29 

9.63 865 

35 

10.36 135 

9.96 234 

6 

29 

10 

5.0 

4.8 

4.7 

32 

9.60 128 

29 

9.63 899 

34 

10.36 101 

9.96 229 

5 

28 

20 

10.0 

9.7 

9.3 

33 

9.60 157 

29 

9.63 934 

35 

10.36 066 

9.96 223 

6 

27 

30 

40 

15.0 
20 0 

14.5 
19 3 

14.0 

18 7 

34 

9.60 186 

29 

29 

9.63 968 

34 

35 

10.36 032 

9.96 218 

5 

26 

50 

25.0 

24^2 

23;3 

35 

9.60 215 

9.64 003 

10.35 997 

9.96 212 

D 

25 







36 

9.60 244 

29 

9.64 037 

34 

10.35 963 

9.96 207 

5 

24 







37 

9.60 273 

29 

9.64 072 

35 

10.35 928 

9.96 201 

6 

23 







38 

9.60 302 

29 

9.64 106 

34 

10.35 894 

9.96 196 

5 

22 







39 

9.60 331 

29 

28 

9.64 140 

34 

35 

10.35 860 

9.96 190 

6 

21 







40 

9.60 359 

9.64 175 

10.35 825 

9.96 185 

O 

20 







41 

9.60 388 

29 

9.64 209 

34 

10.35 791 

9.96 179 

6 

19 







42 

9.60 417 

29 

9.64 243 

34 

10.35 757 

9.96 174 

5 

18 







43 

9.60 446 

29 

9.64 278 

35 

10.35 722 

9.96 168 

6 

17 







44 

9.60 474 

28 

29 

9.64 312 

34 

34 

10.35 688 

9.96 162 

6 

16 







45 

- 9.60 503 

9.64 346 

10.35 654 

9.96 157 

O 

15 



( 


5 


46 

9.60 532 

29 

9.64 381 

35 

10.35 619 

9.96 151 

6 

14 







47 

9.60 561 

29 

9.64 415 

34 

10.35 585 

9.96 146 

5 

13 


6 

0.6 

0.5 

48 

9.60 589 

28 

9.64 449 

34 

10.35 551 

9.96 140 

6 

12 


7 

8 

0.7 
0 8 

0.6 

0 7 

49 

9.60 618 

29 

28 

9.64 483 

34 

34 

10.35 517 

9.96 135 

5 

A 

11 


9 

0^9 

0'.8 

50 

9.60 646 

9.64 517 

10.35 483 

9.96 129 

D 

10 


10 

1.0 

0.8 

51 

9.60 675 

29 

9.64 552 

35 

10.35 448 

9.96 123 

6 

9 


20 

30 

2.0 
3 0 

1.7 
o n. 

52 

9.60 704 

29 

9.64 586 

34 

10.35 414 

9.96 118 

5 

8 


40 

4!o 



53 

9.60 732 

28 

9.64 620 

34 

10.35 380 

9.96 112 

6 

7 


50 

5.0 

4.2 

54 

9.60 761 

29 

28 

9.64 654 

34 

10.35 346 

9.96 107 

5 

A 

6 







55 

9.60 789 

9.64 688 


10.35 312 

9.96 101 

D 

5 







56 

9.60 818 

29 

9.64 722 

34 

10.35 278 

9.96 095 

6 

4 







57 

9.60 846 

28 

9.64 756 

34 

10.35 244 

9.96 090 

5 

3 







58 

9.60 875 

29 

9.64 790 

34 

10.35 210 

9.96 084 

6 

2 







59 

9.60 903 

28 

28 

9.64 824 

34 

34 

10.35 176 

9.96 079 

5 

A 

1 







60 

9.60 931 

9.64 858 

10.35 142 

9.96 073 

O 

0 








L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


66 ’ 











































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


51 


24 ^ 



L Sin 

0 

9.60 931 . 

1 

9.60 960 ■ 

2 

9.60 988 ■ 

3 

9.61 016 ■ 

4 

9.61 045 

5 

9.61 073 

6 

9.61 101 

7 

9.61 129 

8 

9.61 158 

9 

9.61 186 

10 

9.61 214 

11 

9.61 242 

12 

9.61 270 

13 

9.61 298 

14 

9.61 326 

15 

9.61 354 

16 

9.61 382 

17 

9.61 411 

18 

9.61 438 

19 

9.61 466 

20 

9.61 494 

21 

9.61 522 

22 

9.61 550 

23 

9.61 578 

24 

9.61 606 

25 

9.61 634 

26 

9.61 662 

27 

9.61 689 

28 

9.61 717 

29 

9.61 745 

30 

9.61 773 

31 

9.61 800 

32 

9.61 828 

33 

9.61 856 

34 

9.61 883 

35 

9.61 911 

36 

9.61 939 

37 

9.61 966 

38 

9.61 994 

39 

9.62 021 

40 

9.62 049 

41 

9.62 076 

42 

9.62 104 

43 

9.62 131 

44 

9.62 159 

45 

9.62 186 

46 

9.62 214 

47 

9.62 241 

48 

9.62 268 

49 

9.62 296 

^0~ 

9.62 323 

51 

9.62 350 

52 

9.62 377 

53 

9.62 405 

54 

9.62 432 

55 

9.62 459 

56 

9.62 486 

57 

9.62 513 

58 

9.62 541 

59 

9.62 568 

60 

9.62 595 


L Cos 


L Tan c d 


L Cot 

L Cos 

d 


10.35 142 

9.96 073 


60 

10.35 108 

9.96 067 

6 

59 

10.35 074 

9.96 062 

5 

58 

10.35 040 

9.96 056 

6 

57 

10.35 006 

9.96 050 

6 

56 

10.34 972 

9.96 045 

o 

55 

10.34 938 

9.96 039 

6 

54 

10.34 904 

9.96 034 

5 

53 

10.34 870 

9.96 028 

6 

52 

10.34 836 

9.96 022 

6 

51 

10.34 803 

9.96 017 


50 

10.34 769 

9.96 011 

6 

49 

10.34 735 

9.96 005 

6 

48 

10.34 701 

9.96 000 

5 

47 

10.34 667 

9.95 994 

6 

a 

46 

10.34 634 

9.95 988 

D 

45 

10.34 600 

9.95 982 

6 

44 

10.34 566 

9.95 977 

■5 

43 

10.34 533 

9.95 971 

6 

42 

10.34 499 

9.95 965 

6 

41 

10.34 465 

9.95 960 

0 

40 

10.34 432 

9.95 954 

6 

39 

10.34 398 

9.95 948 

6 

38 

10.34 364 

9.95 942 

6 

37 

10.34 331 

9.95 937 

5 

36 

10.34 297 

9.95 931 

0 

35 

10.34 264 

9.95 925 

6 

34 

10.34 230 

9.95 920 

5 

33 

10.34 197 

9.95 914 

6 

32 

10.34 163 

9.95 908 

6 

A 

31 

10.34 130 

9.95 902 

0 

30 

10.34 096 

9.95 897 

5 

29 

10.34 063 

9.95 891 

6 

28 

10.34 029 

9.95 885 

6 

27 

10.33 996 

9.95 879 

6 

A 

26 

10.33 962 

9.95 873 

D 

25 

10.33 929 

9.95 868 

5 

24 

10.33 896 

9.95 862 

6 

23 

10.33 862 

9.95 856 

6 

22 

10.33 829 

9.95 850 

6 

A 

21 

10.33 796 

9.95 844 

U 

20 

10.33 762 

9.95 839 

5 

19 

10.33 729 

9.95 833 

6 

18 

10.33 696 

9.95 827 

6 

17 

10.33 663 

9.95 821 

6 

0 

16 

10.33 629 

9.95 815 


15 

10.33 596 

9.95 810 

5 

14 

10.33 563 

9.95 804 

6 

13 

10.33 530 

9.95 798 

6 

12 

10.33 497 

9.95 792 

6 

6 

11 

10.33 463 

9.95 786 

6 

10 

10.33 430 

9.95 780 

9 

10.33 397 

9.95 775 

5 

8 

10.33 364 

9.95 769 

6 

7 

10.33 331 

9.95 763 

6 

0 

6 

10.33 298 

9.95 757 

6 

5 

10.33 265 

9.95 751 

4 

10.33 232 

9.95 745 

6 

3 

10.33 199 

9.95 739 

6 

2 

10.33 166 

9.95 733 

6 

5 

1 

10.33 133 

9.95 728 


0 

L Tan 

L Sin 

d 

' 


Prop. Pts. 


29 

28 

28 

28 

29 

28 

28 

28 

28 

28 

28 

28 

28 

29 

27 

28 
28 
28 
28 
28 
28 
28 
28 

27 

28 
28 
28 

27 

28 
28 

27 

28 
28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 
27 

27 

28 
27 
27 

27 

28 
27 
27 
27 

27 

28 
27 
27 


9.64 858 
9.64 892 
9.64 926 
9.64 960 
9.64 994 


9.65 028 
9.65 062 
9.65 096 
9.65 130 
9.65 164 



9.65 535 
9.65 568 
9.65 602 
9.65 636 
9.65 669 


9.65 703 
9.65 736 
9.65 770 
9.65 803 
9.65 837 


9.65 870 
9.65 904 
9.65 937 

9.65 971 

9.66 004 


9.66 038 
9.66 071 
9.66 104 
9.66 138 
9.66 171 


9.66 204 
9.66 238 
9.66 271 
9.66 304 
9.66 337 


9.66 371 
9.66 404 
9.66 437 
9.66 470 
9.66 503 


9.66 537 
9.66 570 
9.66 603 
9.66 636 
9.66 669 


9.66 702 
9.66 735 
9.66 768 
9.66 801 
9.66 834 


9.66 867 


L Cot 


c d 


34 

3.4 
4.0 

4.5 
5.1 
5.7 

11.3 
17.0 
22.7 

28.3 


33 

3.3 
3.8 

4.4 
5.0 

5.5 

11.0 

16.5 

22.0 

27.5 


" 

29 

28 

27 

6 

2.9 

2.8 

2.7 

7 

3.4 

3.3 

3.2 

8 

3.9 

3.7 

3.6 

9 

4.4 

4.2 

4.0 

10 

4.8 

4.7 

4.5 

20 

9.7 

9.3 

9.0 

30 

14.5 

14.0 

13.5 

40 

19.3 

18.7 

18.0 

50 

24.2 

23.3 

22.5 


Prop. Pts. 


66 ' 
























































































52 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


25 ° 



L Sin 

d 

L Tan c d L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.62 595 
9.62 622 
9.62 649 
9.62 676 
9.62 703 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

26 

27 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

26 

27 

26 

27 

26 

27 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

26 

27 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

26 

9.66 867 
9.66 900 
9.66 933 
9.66 966 
9.66 999 

33 

33 

33 

33 

33 

33 

33 

33 

32 

33 

33 

33 

33 

32 

33 

33 

33 

32 

33 
33 

32 

33 
33 

32 

33 

32 

33 
33 

32 

33 

32 

33 

32 

33 
32 

32 

33 

32 

33 
32 

32 

33 
32 

32 

33 

32 

32 

32 

33 
32 

32 

32 

32 

33 
32 

32 

32 

32 

32 

32 

10.33 133 
10.33 100 
10.33 067 
10.33 034 
10.33 001 

9.95 728 
9.95 722 
9.95 716 
9.95 710 
9.95 704 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

5 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

7 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

6 

7 

6 

6 

6 

6 

6 

6 

7 

6 

6 

6 

60 

59 

58 

57 

56 

" 33 32 

6 3.3 3.2 

7 3.8 3.7 

8 4.4 4.3 

8 5.0 4.8 

10 5.5 5.3 

20 11.0 10.7 

30 16.5 16.0 

40 22.0 21.3 

50 27.5 26.7 

" 27 26 

6 2.7 2.6 

7 3.2 3.0 

8 3.6 3.5 

9 4.0 3.9 

10 4.5 4.3 

20 9.0 8.7 

30 13.5 13.0 

40 18.0 17.3 

50 22.5 21.7 

"765 

6 0.7 0.6 0.5 

7 0.8 0.7 0.6 

8 0.9 0.8 0.7 

9 1.0 0.9 0.8 

10 1.2 1.0 0.8 

20 2.3 2.0 1.7 

30 3.5 3.0 2.5 

40 4.7 4.0 3.3 

50 5.8 5.0 4.2 

5 

6 

7 

8 

9 

9.62 730 
9.62 757 
9.62 784 
9.62 811 
9.62 838 

9.67 032 
9.67 065 
9.67 098 
9.67 131 
9.67 163 

10.32 968 
10.32 935 
10.32 902 
10.32 869 
10.32 837 

9.95 698 
9.95 692 
9.95 686 
9.95 680 
9.95 674 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.62 865 
9.62 892 
9.62 918 
9.62 945 
9.62 972 

9.67 196 
9.67 229 
9.67 262 
9.67 295 
9.67 327 

10.32 804 
10.32 771 
10.32 738 
10.32 705 
10.32 673 

9.95 668 
9.95 663 
9.95 657 
9.95 651 
9.95 645 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.62 999 

9.63 026 
9.63 052 
9.63 079 
9.63 106 

9.67 360 
9.67 393 
9.67 426 
9.67 458 
9.67 491 

10.32 640 
10.32 607 
10.32 574 
10.32 542 
10.32 509 

9.95 639 
9.95 633 
9.95 627 
9.95 621 
9.95 615 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.63 133 
9.63 159 
9.63 186 
9.63 213 
9.63 239 

9.67 524 
9.67 556 
9.67 589 
9.67 622 
9.67 654 

10.32 476 
10.32 444 
10.32 411 
10.32 378 
10.32 346 

9.95 609 
9.95 603 
9.95 597 
9.95 591 
9.95 585 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.63 266 
9.63 292 
9.63 319 
9.63 345 
9.63 372 

9.67 687 
9.67 719 
9.67 752 
9.67 785 
9.67 817 

10.32 313 
10.32 281 
10.32 248 
10.32 215 
10..32 183 

9.95 579 
9.95 573 
9.95 567 
9.95 561 
9.95 555 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.63 398 
9.63 425 
9.63 451 
9.63 478 
9.63 504 

9.67 850 
9.67 882 
9.67 915 
9.67 947 
9.67 980 

10.32 150 
10.32 118 
10.32 085 
10.32 053 
10.32 020 

9.95 549 
9.95 543 
9.95 537 
9.95 531 
9.95 525 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.63 531 
9.63 557 
9.63 583 
9.63 610 
9.63 636 

9.68 012 
9.68 044 
9.68 077 
9.68 109 
9.68 142 

10.31 988 
10.31 956 
10.31 923 
10.31 891 
10.31 858 

9.95 519 
9.95 513 
9.95 507 
9.95 500 
9.95 494 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.63 662 
9.63 689 
9.63 715 
9.63 741 
9.63 767 

9.68 174 
9.68 206 
9.68 239 
9.68 271 
9.68 303 

10.31 826 
10.31 794 
10.31 761 
10.31 729 
10.31 697 

9.95 488 
9.95 482 
9.95 476 
9.95 470 
9.95 464 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.63 794 
9.63 820 
9.63 846 
9.63 872 
9.63 898 

9.68 336 
9.68 368 
9.68 400 
9.68 432 
9.68 465 

10.31 664 
10.31 632 
10.31 600 
10.31 568 
10.31 535 

9.95 458 
9.95 452 
9.95 446 
9.95 440 
9.95 434 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.63 924 
9.63 950 

9.63 976 

9.64 002 
9.64 028 

9.68 497 
9.68 529 
9.68 561 
9.68 593 
9.68 626 

10.31 503 
10.31 471 
10.31 439 
10.31 407 
10.31 374 

9.95 427 
9.95 421 
9.95 415 
9.95 409 
9.95 403 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.64 054 
9.64 080 
9.64 106 
9.64 132 
9.64 158 

9.68 658 
9.68 690 
9.68 722 
9.68 754 
9.68 786 

10.31 342 
10.31 310 
10.31 278 
10.31 246 
10.31 214 

9.95 397 
9.95 391 
9.95 384 
9.95 378 
9.95 372 

5 

4 

3 

2 

1 

60 

9.64 184 

9.68 818 

10.31 182 

9.95 366 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 


Prop. Pts. 


81 ' 











































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


53 


26 ° 



L Sin j d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.64 184 
9.64 210 
9.64 236 
9.64 262 
9.64 288 

26 

26 

26 

26 

25 

26 
26 
26 
26 

25 

26 
26 

25 

26 
26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 
25 

25 

26 

25 

25 

26 
25 
25 

25 

26 
25 
25 
25 

25 

25 

26 
25 
25 

25 

25 

25 

25 

25 

25 

25 

25 

25 

24 

25 
25 
25 
25 
25 

9.68 818 
9.68 850 
9.68 882 
9.68 914 
9.68 946 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

32 

31 

32 
32 
32 
32 

31 

32 
32 
32 

31 

32 
32 

31 

32 
32 

31 

32 

31 

32 
32 

31 

32 

31 

32 

31 

32 

31 

32 

31 

32 

31 

31 

32 

31 

32 

31 

31 

32 
31 

31 

32 
31 

31 

31 

32 

10.31 182 
10.31 150 
10.31 118 
10.31 086 
10.31 054 

9.95 366 
9.95 360 
9.95 354 
9.95 348 
9.95 341 

6 

6 

6 

7 

6 

6 

6 

6 

7 

6 

6 

6 

6 

7 

6 

6 

6 

7 

6 

6 

6 

7 

6 

6 

6 

7 

6 

6 

7 

6 

6 

6 

7 

6 

6 

7 

6 

6 

7 

6 

6 

7 

6 

7 

6 

6 

7 

6 

6 

7 

6 

7 

6 

6 

7 

6 

7 

6 

6 

7 

60 

59 

58 

57 

56 

" 32 31 

6 3.2 3.1 

7 3.7 3.6 

8 4.3 4.1 

9 4.8 4.6 

10 5.3 5.2 

20 10.7 10.3 

30 16.0 15.5 

40 21.3 20.7 

50 26.7 25.8 

" 26 25 24 

6 2.6 2.5 2.4 

7 3.0 2.9 2.8 

8 3.5 3.3 3.2 

9 3.9 3.8 3.6 

10 4.3 4.2 4.0 

20 8.7 8.3 8.0 

30 13.0 12.5 12.0 

40 17.3 16.7 16.0 

50 21.7 20.8 20.0 

"76 

6 0.7 0.6 

7 0.8 0.7 

8 0.9 0.8 

9 1.0 0.9 

10 1.2 1.0 

20 2.3 2.0 

30 3.5 3.0 

40 4.7 4.0 

50 5.8 5.0 

5 

6 

7 

8 

9 

9.64 313 
9.64 339 
9.64 365 
9.64 391 
9.64 417 

9.68 978 

9.69 010 
9.69 042 
9.69 074 
9.69 106 

10.31 022 
10.30 990 
10.30 958 
10.30 926 
10.30 894 

9.95 335 
9.95 329 
9.95 323 
9.95 317 
9.95 310 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.64 442 
9.64 468 
9.64 494 
9.64 519 
9.64 545 

9.69 138 
9.69 170 
9.69 202 
9.69 234 
9.68 266 

10.30 862 
10.30 830 
10.30 798 
10.30 766 
10.30 734 

9.95 304 
9.95 298 
9.95 292 
9.95 286 
9.95 279 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.64 571 
9.64 596 
9.64 622 
9.64 647 
9.64 673 

9.69 298 
9.69 329 
9.69 361 
9.69 393 
9.69 425 

10.30 702 
10.30 671 
10.30 639 
10.30 607 
10.30 575 

9.95 273 
9.95 267 
9.95 261 
9.95 254 
9.95 248 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.64 698 
9.64 724 
9.64 749 
9.64 775 
9.64 800 

9.69 457 
9.69 488 
9.69 520 
9.69 552 
9.69 584 

10.30 543 
10.30 512 
10.30 480 
10.30 448 
10.30 416 

9.95 242 
9.95 236 
9.95 229 
9.95 223 
9.95 217 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.64 826 
9.64 851 
9.64 877 
9.64 902 
9.64 927 

9.69 615 
9.69 647 
9.69 679 
9.69 710 
9.69 742 

10.30 385 
10.30 353 
10.30 321 
10.30 290 
10.30 258 

9.95 211 
9.95 204 
9.95 198 
9.95 192 
9.95 185 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.64 953 

9.64 978 

9.65 003 
9.65 029 
9.65 054 

9.69 774 
9.69 805 
9.69 837 
9.69 868 
9.69 900 

10.30 226 
10.30 195 
10.30 163 
10.30 132 
10.30 100 

9.95 179 
9.95 173 
9.95 167 
9.95 160 
9.95 154 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.65 079 
9.65 104 
9.65 130 
9.65 155 
9.65 180 

9.69 932 
9.69 963 

9.69 995 

9.70 026 
9.70 058 

10.30 068 
10..30 037 
10.30 005 
10.29 974 
10.29 942 

9.95 148 
9.95 141 
9.95 135 
9.95 129 
9.95 122 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.65 205 
9.65 230 
9.65 255 
9.65 281 
9.65 306 

9.70 089 
9.70 121 
9.70 152 
9.70 184 
9.70 215 

10.29 911 
10.29 879 
10.29 848 
10.29 816 
10.29 785 

9.95 116 
9.95 110 
9.95 103 
9.95 097 
9.95 090 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.65 331 
9.65 356 
9.65 381 
9.65 406 
9.65 431 

9.70 247 
9.70 278 
9.70 309 
9.70 341 
9.70 372 

10.29 753 
10.29 722 
10.29 691 
10.29 659 
10.29 628 

9.95 084 
9.95 078 
9.95 071 
9.95 065 
9.95 059 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.65 456 
9.65 481 
9.65 506 
9.65 531 
9.65 556 

9.70 404 
9.70 435 
9.70 466 
9.70 498 
9.70 529 

10.29 596 
10.29 565 
10.29 .534 
10.29 .502 
10.29 471 

9.95 052 
9.95 046 
9.95 039 
9.95 033 
9.95 027 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.65 580 
9.65 605 
9.65 630 
9.65 655 
9.65 680 

9.70 560 
9.70 592 
9.70 623 
9.70 654 
9.70 685 

10.29 440 
10.29 408 
10.29 377 
10.29 346 
10.29 315 

9.95 020 
9.95 014 
9.95 007 
9.95 001 
9.94 995 

5 

4 

3 

2 

1 

60 

9.65 705 

9.70 717 

10.29 283 

9.94 988 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


63 * 



















































































54 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


27 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.65 705 


9.70 717 


10.29 283 

9.94 988 


60 

1 

9.65 729 

24 

9.70 748 

31 

10.29 252 

9.94 982 

6 

59 

2 

9.65 754 

25 

9.70 779 

31 

10.29 221 

9.94 975 

7 

58 

3 

9.65 779 

25 

9.70 810 

31 

10.29 190 

9.94 969 

6 

57 

4 

9.65 804 

25 

24 

9.70 841 

31 

32 

10.29 159 

9.94 962 

7 

6 

56 

5 

9.65 828 

9.70 873 

10.29 127 

9.94 956 

55 

6 

9.65 853 

25 

9.70 904 

31 

10.29 096 

9.94 949 

7 

45 

7 

9.65 878 

25 

9.70 935 

31 

10.29 065 

9.94 943 

6 

53 

8 

9.65 902 

24 

9.70 966 

31 

10.29 034 

9.94 936 

7 

52 

9 

9.65 927 

25 

9.70 997 

31 

31 

10.29 003 

9.94 930 

6 

7 

51 

10 

9.65 952 


9.71 028 

10.28 972 

9.94 923 


50 

11 

9,65 976 

24 

9.71 059 

31 

10.28 941 

9.94 917 

6 

49 

12 

9.66 001 

25 

9.71 090 

31 

10.28 910 

9.94 911 

6 

48 

13 

9.66 025 

24 

9.71 121 

31 

10.28 879 

9.94 904 

7 

47 

14 

9.66 050 

25 

25 

9.71 153 

32 

31 

10.28 847 

9.94 898 

6 

7 

46 

15 

9.66 075 

9.71 184 

10.28 816 

9.94 891 

i 

45 

16 

9.66 099 

24 

9.71 215 

31 

10.28 785 

9.94 885 

6 

44 

17 

9.66 124 

25 

9.71 246 

31 

10.28 754 

9.94 878 

7 

43 

18 

9.66 148 

24 

9.71 277 

31 

10.28 723 

9.94 871 

7 

42 

19 

9.66 173 

25 

24 

9.71 308 

31 

31 

10.28 692 

9.94 865 

6 

7 

41 

20 

9.66 197 

9.71 339 

10.28 661 

9.94 858 


40 

21 

9.66 221 

24 

9.71 370 

31 

10.28 630 

9.94 852 

6 

39 

22 

9.66 246 

25 

9.71 401 

31 

10.28 599 

9.94 845 

7 

38 

23 

9.66 270 

24 

9.71 431 

30 

10.28 569 

9.94 839 

6 

37 

24 

9.66 295 

25 

24 

9.71 462 

31 

31 

10.28 538 

9.94 832 

7 

36 

25 

9.66 319 

9.71 493 

10.28 507 

9.94 826 

D 

35 

26 

9.66 343 

24 

9.71 524 

31 

10.28 476 

9.94 819 

7 

34 

27 

9.66 368 

25 

9.71 555 

31 

10.28 445 

9.94 813 

6 

33 

28 

9.66 392 

24 

9.71 586 

31 

10.28 414 

9.94 806 

7 

32 

29 

9.66 416 

24 

25 

9.71 617 

31 

31 

10.28 383 

9.94 799 

7 

31 

30 

9.66 441 

9.71 648 

10.28 352 

9.94 793 


30 

31 

9.66 465 

24 

9.71 679 

31 

10.28 321 

9.94 786 

7 

29 

32 

9.66 489 

24 

9.71 709 

30 

10.28 291 

9.94 780 

6 

28 

33 

9.66 513 

24 

9.71 740 

31 

10.28 260 

9.94 773 

7 

27 

34 

9.66 537 

24 

25 

9.71 771 

31 

31 

10.28 229 

9.94 767 

6 

7 

26 

35 

9.66 562 

9.71 802 

10.28 198 

9.94 760 

( 

25 

36 

9.66 586 

24 

9.71 833 

31 

10.28 167 

9.94 753 

7 

24 

37 

9.66 610 

24 

9.71 863 

30 

10.28 137 

9.94 747 

6 

23 

38 

9.66 634 

24 

9.71 894 

31 

10.28 106 

9.94 740 

7 

22 

39 

9.66 658 

24 

24 

9.71 925 

31 

30 

10.28 075 

9.94 734 

6 

7 

21 

40 

9.66 682 

9.71 955 

10.28 045 

9.94 727 

1 

20 

41 

9.66 706 

24 

9.71 986 

31 

10.28 014 

9,94 720 

7 

19 

42 

9.66 731 

25 

9.72 017 

31 

10.27 983 

9.94 714 

6 

18 

43 

9.66 755 

24 

9,72 048 

31 

10.27 952 

9.94 707 

7 

17 

44 

9.66 779 

24 

9.72 078 

30 

10.27 922 

9.94 700 

7 

16 



24 


31 





45 

9.66 803 

9.72 109 

10.27 891 

9.94 694 


15 

46 

9.66 827 

24 

9.72 140 

31 

10.27 860 

9.94 687 

7 

14 

47 

9.66 851 

24 

9.72 170 

30 

10.27 830 

9.94 680 

7 

13 

48 

9.66 875 

24 

9.72 201 

31 

10.27 799 

9.94 674 

6 

12 

49 

9.66 899 

24 

23 

9.72 231 

30 

31 

10.27 769 

9.94 667 

7 

n 

11 

50 

9.66 922 

9.72 262 

10.27 738 

9.94 660 

4 

10 

51 

9.66 946 

24 

9.72 293 

31 

10.27 707 

9.94 654 

6 

9 

52 

9.66 970 

24 

9.72 323 

30 

10.27 677 

9.94 647 

7 

8 

53 

9.66 994 

24 

9.72 354 

31 

10.27 646 

9.94 640 

7 

7 

54 

9.67 018 

24 

24 

9.72 384 

30 

31 

10.27 616 

9.94 634 

6 

7 

6 

55 

9.67 042 

9.72 415 

10.27 585 

9.94 627 

4 

5 

56 

9.67 066 

24 

9.72 445 

30 

10.27 555 

9.94 620 

7 

4 

57 

9.67 090 

24 

9.72 476 

31 

10.27 524 

9.94 614 

6 

3 

58 

9.67 113 

23 

9.72 506 

30 

10.27 494 

9.94 607 

7 

2 

59 

9.67 137 

24 

9.72 537 

31 

10.27 463 

9.94 600 

7 

1 



24 


30 





60 

9.67 161 

9.72 567 

10.27 433 

9.94 593 


0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

/ 


Prop. Pts. 



32 

31 

30 

6 

3.2 

3.1 

3.0 

7 

3.7 

3.6 

3.5 

8 

4.3 

4.1 

4.0 

9 

4.8 

4.6 

4.5 

10 

5.3 

5.2 

5.0 

20 

10.7 

10.3 

10.0 

30 

16.0 

15.5 

15.0 

40 

21.3 

20.7 

20.0 

50 

26.7 

25.8 

25.0 



25 

24 

23 

6 

2.5 

2.4 

2.3 

7 

2.9 

2.8 

2.7 

8 

3.3 

3.2 

3.1 

9 

3.8 

3.6 

3.4 

10 

4.2 

4.0 

3.8 

20 

8.3 

8.0 

7.7 

30 

12.5 

12.0 

11.5 

40 

16.7 

16.0 

15.3 

50 

20.8 

20.0 

19.2 


Prop. Pts. 


62 ' 





































































VI 


FIVE-PLACE LOGARITHMS OF FUx\CTIONS 


55 


28 ^ 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.67 161 


9.72 567 


10.27 433 

9.94 593 


60 

1 

9.67 185 

24 

9.72 598 

31 

10.27 402 

9.94 587 

6 

59 

2 

9.67 208 

23 

9.72 628 

30 

10.27 372 

9.94 580 

7 

58 

3 

9.67 232 

24 

9.72 659 

31 

10.27 341 

9.94 573 

7 

57 

4 

9.67 256 

24 

24 

9.72 689 

30 

31 

10.27 311 

9.94 567 

6 

56 

5 

9.67 280 

9.72 720 

10.27 280 

9.94 560 


55 

6, 

9.67 303 

23 

9.72 750 

30 

10.27 250 

9.94 553 

7 

54 

7 

9.67 327 

24 

9.72 780 

30 

10.27 220 

9.94 546 

7 

53 

8 

9.67 350 

23 

9.72 811 

31 

10.27 189 

9.94 540 

6 

52 

9 

9.67 374 

24 

24 

9.72 841 

30 

31 

10.27 159 

9.94 533 

7 

7 

51 

10 

9.67 398 

9.72 872 

10.27 128 

9.94 526 

4 

50 

11 

9.67 421 

23 

9.72 902 

30 

10.27 098 

9.94 519 

7 

49 

12 

9.67 445 

24 

9.72 932 

30 

10.27 068 

9.94 513 

6 

48 

13 

9.67 468 

23 

9.72 963 

31 

10.27 037 

9.94 506 

7 

47 

14 

9.67 492 

24 

23 

9.72 993 

30 

30 

10.27 007 

9.94 499 

7 

7 

46 

15 

9.67 515 

9.73 023 

10.26 977 

9.94 492 

4 

45 

16 

9.67 539 

24 

9.73 054 

31 

10.26 946 

9.94 485 

7 

44 

17 

9.67 562 

23 

9.73 084 

30 

10.26 916 

9.94 479 

6 

43 

18 

9.67 586 

24 

9.73 114 

30 

10.26 886 

9.94 472 

7 

42 

19 

9.67 609 

23 

24 

0.73 144 

30 

31 

10.26 856 

9.94 465 

7 

7 

41 

20 

9.67 633 

9.73 175 

10.26 825 

9.94 458 

4 

40 

21 

9.67 656 

23 

9.73 205 

30 

10.26 795 

9.94 451 

7 

39 

22 

9.67 680 

24 

9.73 235 

30 

10.26 765 

9.94 445 

6 

38 

23 

9.67 703 

23 

9.73 265 

30 

10.26 735 

9.94 438 

7 

37 

24 

9.67 726 

23 

24 

9.73 295 

30 

10.26 705 

9.94 431 

7 

7 

36 

25 

9.67 750 

9.73 326 

31 

10.26 674 

9.94 424 

4 

35 

26 

9.67 773 

23 

9.73 356 

30 

10.26 644 

9.94 417 

7 

34 

27 

9.67 796 

23 

9.73 386 

30 

10.26 614 

9.94 410 

7 

33 

28 

9.67 820 

24 

9.73 416 

30 

10.26 584 

9.94 404 

6 

32 

29 

9.67 843 

23 

9.73 446 

30 

10.26 554 

9.94 397 

7 

7 

31 

30 

9.67 866 


9.73 476 

oU 

10.26 524 

9.94 390 


30 

31 

9.67 890 

24 

9.73 507 

31 

10.26 493 

9.94 383 

7 

29 

32 

9.67 913 

23 

9.73 537 

30 

10.26 463 

9.94 376 

7 

28 

33 

9.67 936 

23 

9.73 567 

30 

10.26 433 

9.94 369 

7 

27 

34 

9.67 959 

23 

9.73 597 

30 

30 

10.26 403 

9.94 362 

7 

7 

26 

35 

9.67 982 


9.73 627 

10.26 373 

9.94 355 


25 

36 

9.68 006 

24 

9.73 657 

30 

10.26 343 

9.94 349 

6 

24 

37 

9.68 029 

23 

9.73 687 

30 

10.26 313 

9.94 342 

7 

23 

38 

9.68 052 

23 

9.73 717 

30 

10.26 283 

9.94 335 

7 

22 

39 

9.68 075 

23 

9Q 

9.73 747 

30 

10.26 253 

9.94 328 

7 

7 

21 

40 

9.68 098 


9.73 777 

OU 

10.26 223 

9.94 321 


20 

41 

9.68 121 

23 

9.73 807 

30 

10.26 193 

9.94 314 

7 

19 

42 

9.68 144 

23 

9.73 837 

30 

10.26 163 

9.94 307 

7 

18 

43 

9.68 167 

23 

9.73 867 

30 

10.26 133 

9.94 300 

7 

17 

44 

9.68 190 

23 

OQ 

9.73 897 

30 

10.26 103 

9.94 293 

7 

7 

16 

45 

9.68 213 


9.73 927 

OU 

10.26 073 

9.94 286 


15 

46 

9.68 237 

24 

9.73 957 

30 

10.26 043 

9.94 279 

7 

14 

47 

9.68 260 

23 

9.73 987 

30 

10.26 013 

9.94 273 

6 

13 

48 

9.68 283 

23 

9.74 017 

30 

10.25 983 

9.94 266 

7 

12 

49 

9.68 305 

22 

OO 

9.74 047 

30 

10.25 953 

9.94 259 

7 

7 

11 

50 

9.68 328 

Jo 

9.74 077 

OU 

10.25 923 

9.94 252 


10 

51 

9.68 351 

23 

9.74 107 

30 

10.25 893 

9.94 245 

7 

9 

52 

9.68 374 

23 

9.74 137 

30 

10.25 863 

9.94 238 

7 

8 

53 

9.68 397 

23 

9.74 166 

29 

10.25 834 

9.94 231 

7 

7 

54 

9.68 420 

23 

OQ 

9.74 196 

30 

10.25 804 

9.94 224 

7 

7 

6 

55 

9.68 443 

Jo 

9.74 226 

OU 

10.25 774 

9.94 217 


5 

56 

9.68 466 

23 

9.74 256 

30 

10.25 744 

9.94 210 

7 

4 

57 

9.68 489 

23 

9.74 286 

30 

10.25 714 

9.94 203 

7 

3 

58 

9.68 512 

23 

9.74 316 

30 

10.25 684 

9.94 196 

7 

2 

59 

9.68 534 

22 

OO 

9.74 345 

29 

•in 

10.25 655 

9.94 189 

7 

7 

1 

60 

9.68 557 

Jo 

9.74 375 

OU 

10.25 625 

9.94 182 


0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 


Prop. Pts. 


>' 

31 

30 

29 

0 

3.1 

3.0 

2.9 

7 

3.6 

3.5 

3.4 

8 

4.1 

4.0 

3.9 

9 

4.6 

4.5 

4.4 

10 

5.2 

5.0 

4.8 

20 

10.3 

10.0 

9.7 

30 

15.5 

15.0 

14.5 

40 

20.7 

20.0 

19.3 

50 

25.8 

25.0 

24.2 


" 

24 

23 

22 

6 

2.4 

2.3 

2.2 

7 

2.8 

2.7 

2.6 

8 

3.2 

3.1 

2.9 

9 

3.6 

3.4 

3.3 

10 

4.0 

3.8 

3.7 

20 

8.0 

7.7 

7.3 

30 

12.0 

11.5 

11.0 

40 

16.0 

15.3 

14.7 

50 

20.0 

19.2 

18.3 


Prop. Pts. 


er 





















































































56 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


29 ° 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.68 557 
9.68 580 
9.68 603 
9.68 625 
9.68 648 

23 

23 

22 

23 

23 

23 

22 

23 

23 

22 

23 

22 

23 

23 

22 

23 

22 

23 

22 

23 

22 

23 

22 

23 

22 

22 

23 

22 

23 

22 

22 

23 

22 

22 

22 

23 

22 

22 

22 

22 

23 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

22 

9.74 375 
9.74 405 
9.74 435 
9.74 465 
9.74 494 

30 

30 

30 

29 

30 

30 

29 

30 
30 
30 

29 

30 
30 

29 

30 

30 

29 

30 

29 

30 

29 

30 
30 

29 

30 

29 

30 

29 

30 

29 

30 

29 

30 
29 

29 

30 

29 

30 
29 

29 

30 

29 

30 
29 

29 

30 
29 

29 

29 

30 

29 

29 

29 

30 
29 

29 

29 

30 

29 

29 

10.25 625 
10.25 595 
10.25 565 
10.25 535 
10.25 506 

9.94 182 
9.94 175 
9.94 168 
9.94 161 
9.94 154 

7 

7 

7 

7 

- 7 

7 

7 

7 

7 

■ 7 

7 

7 

8 

7 

7 

7 

7 

7 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

7 

8 

7 

7 

7 

7 

8 

7 

7 

7 

8 

7 

7 

7 

7 

8 

7 

7 

8 

7 ■ 

7 

7 

8 

7 

60 

59 

58 

57 

56 

" 30 29 

6 3.0 2.9 

7 3.5 3.5 

8 4.0 3.9 

9 4.5 4.4 

10 5.0 4.8 

20 10.0 9.7 

30 15.0 14.5 

40 20.0 19.3 

50 25.0 24.2 

" 23 22 

6 2.3 2.2 

7 2.7 2.6 

8 3.1 2.9 

9 3.4 3.3 

10 3.8 3.7 

20 7.7 7.3 

30 11.5 11.0 

40 15.3 14.7 

50 19.2 18.3 

"87 

6 0.8 0.7 

7 0.9 0.8 

8 1.1 0.9 

9 1.2 1.0 

10 1.3 1.2 

20 2.7 2.3 

30 4.0 3.5 

40 5.3 4.7 

50 6.7 5.8 

5 

6 

7 

8 

9 

9.68 671 
9.68 694 
9.68 716 
9.68 739 
9.68 762 

9.74 524 
9.74 554 
9.74 583 
9.74 613 
9.74 643 

10.25 476 
10.25 446 
10.25 417 
10.25 387 
10.25 357 

9.94 147 
9.94 140 
9.94 133 
9.94 126 
9.94 119 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.68 784 
9.68 807 
9.68 829 
9.68 852 
9.68 875 

9.74 673 
9.74 702 
9.74 732 
9.74 762 
9.74 791 

10.25 327 
10.25 298 
10.25 268 
10.25 238 
10.25 209 

9.94 112 
9.94 105 
9.94 098 
9.94 090 
9.94 083 

SO 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.68 897 
9.68 920 
9.68 942 
9.68 965 
9.68 987 

9.74 821 
9.74 851 
9.74 880 
9.74 910 
9.74 939 

10.25 179 
10.25 149 
10.25 120 
10.25 090 
10.25 061 

9.94 076 
9.94 069 
9.94 062 
9.94 055 
9.94 048 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.69 010 
9.69 032 
9.69 055 
9.69 077 
9.69 100 

9.74 969 

9.74 998 

9.75 028 
9.75 058 
9.75 087 

10.25 031 
10.25 002 
10.24 972 
10.24 942 
10.24 913 

9.94 041 
9.94 034 
9.94 027 
9.94 020 
9.94 012 

40 

39 

38 

37 

36 

35 

34 

33 

32 

31 

30 

29 

28 

27 

26 

25 

24 

23 

22 

21 

20 

19 

18 

17 

16 

15 

14 

13 

12 

11 

10 

9 

8 

7 

6 

5 

4 

3 

2 

1 

0 

25 

26 

27 

28 

29 

30 

31 

32 

33 

34 

9.69 122 
9.69 144 
9.69 167 
9.69 189 
9.69 212 

9.75 117 
9.75 146 
9.75 176 
9.75 205 
9.75 235 

10.24 883 
10.24 854 
10.24 824 
10.24 795 
10.24 765 

9.94 005 
9.93 998 
9.93 991 
9.93 984 
9.93 977 

9.69 234 
9.69 256 
9.69 279 
9.69 301 
9.69 323 

9.75 264 
9.75 294 
9.75 323 
9.75 353 
9.75 382 

10.24 736 
10.24 706 
10.24 677 
10.24 647 
10.24 618 

9.93 970 
9.93 963 
9.93 955 
9.93 948 
9.93 941 

35 

36 

37 

38 

39 

9.69 345 
9.69 368 
9.69 390 
9.69 412 
9.69 434 

9.75 411 
9.75 441 
9.75 470 
9.75 500 
9.75 529 

10.24 589 
10.24 559 
10.24 530 
10.24 500 
10.24 471 

9.93 934 
9.93 927 
9.93 920 
9.93 912 
9.93 905 

40 

41 

42 

43 

44 

9.69 456 
9.69 479 
9.69 501 
9.69 523 
9.69 545 

9.75 558 
9.75 588 
9.75 617 
9.75 647 
9.75 676 

10.24 442 
10.24 412 
10.24 383 
10.24 353 
10.24 324 

9.93 898 
9.93 891 
9.93 884 
9.93 876 
9.93 869 

45 

46 

47 

48 

49 

9.69 567 
9.69 589 
9.69 611 
9.69 633 
9.69 655 

9.75 705 
9.75 735 
9.75 764 
9.75 793 
9.75 822 

10.24 295 
10.24 265 
10.24 236 
10.24 207 
10.24 178 

9.93 862 
9.93 855 
9.93 847 
9.93 840 
9.93 833 

60 

51 

52 

53 

54 

9.69 677 
9.69 699 
9.69 721 
9.69 743 
9.69 765 

9.75 852 
9.75 881 
9.75 910 
9.75 939 
9.75 969 

10.24 148 
10.24 119 
10.24 090 
10.24 061 
10.24 031 

9.93 826 
9.93 819 
9.93 811 
9.93 804 
9.93 797 

55 

56 

57 

58 

59 

9.69 787 
9.69 809 
9.69 831 
9.69 853 
9.69 875 

9.75 998 

9.76 027 
9.76 056 
9.76 086 
9.76 115 

10.24 002 
10.23 973 
10.23 944 
10.23 914 
10.23 885 

9.93 789 
9.93 782 
9.93 775 
9.93 768 
9.93 760 

60 

9.69 897 

9.76 144 

10.23 856 

9.93 753 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' r 

Prop. Pts. 


60 ' 
















































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


0 / 


30 ° 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.69 897 
9.69 919 
9.69 941 
9.69 963 
9.69 984 

22 

22 

22 

21 

22 

22 

22 

22 

21 

22 

22 

22 

21 

22 

22 

21 

22 

21 

22 

22 

21 

22 

21 

22 

21 

22 

21 

22 

21 

22 

21 

22 

21 

22 

21 

21 

22 

21 

21 

22 

21 

21 

21 

22 

21 

21 

21 

22 

21 

21 

21 

21 

21 

22 

2-1 

21 

21 

21 

21 

21 

9.76 144 
9.76 173 
9.76 202 
9.76 231 
9.76 261 

29 

29 

29 

30 
29 

29 

29 

29 

29 

29 

29 

29 

29 

29 

29 

29 

30 
29 
29 
28 

29 

29 

29 

29 

29 

29 

29 

29 

29 

29 

29 

29 

28 

29 

29 

29 

29 

29 

28 

29 

29 

29 

29 

28 

29 

29 

29 

28 

29 

29 

28 

29 

29 

29 

28 

29 

28 

29 

29 

28 

10.23 856 
10.23 827 
10.23 798 
10.23 769 
10.23 739 

9.93 753 
9.93 746 
9.93 738 
9.93 731 
9.93 724 

7 

8 

7 

7 

7 

8 

7 

7 

8 

7 

7 

8 

7 

8 

7 

7 

8 

7 

7 

8 

7 

8 

7 

7 

8 

7 

8 

7 

8 

7 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

7 

8 

8 

7 

8 

7 

8 

7 

60 

59 

58 

57 

56 

" 30 29 28 

6 3.0 2.9 2.8 

7 3.5 3.4 3.3 

8 4.0 3.9 3.7 

9 4.5 4.4 4.2 

10 5.0 4.8 4.7 

20 10.0 9.7 9.3 

30 15.0 14.5 14.0 

40 20.0 19.3 18.7 

50 25.0 24.2 23.3 

" 22 21 

6 2.2 2.1 

7 2.6 2.4 

8 2.9 2.8 

9 3.3 3.2 

10 3.7 3.5 

20 7.3 7.0 

30 11.0 10.5 

40 14.7 14.0 

50 18.3 17.5 

"87 

6 0.8 0.7 

7 0.9 0.8 

8 1.1 0.9 

9 1.2 1.0 

10 1.3 1.2 

20 2.7 2.3 

30 4.0 3.5 

40 5.3 4.7 

50 6.7 5.8 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

9.70 006 
9.70 028 
9.70 050 
9.70 072 
9.70 093 

9.76 290 
9.76 319 
9.76 348 
9.76 377 
9.76 406 

10.23 710 
10.23 681 
10.23 652 
10.23 623 
10.23 594 

9.93 717 
9.93 709 
9.93 702 
9.93 695 
9.93 687 

55 

54 

53 

52 

51 

9.70 115 
9.70 137 
9.70 159 
9.70 180 
9.70 202 

9.76 435 
9.76 464 
9.76 493 
9.76 522 
9.76 551 

10.23 565 
10.23 536 
10.23 507 
10.23 478 
10.23 449 

9.93 680 
9.93 673 
9.93 665 
9.93 658 
9.93 650 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.70 224 
9.70 245 
9.70 267 
9.70 288 
9.70 310 

9.76 580 
9.76 609 
9.76 639 
9.76 668 
9.76 697 

10.23 420 
10.23 391 
10.23 361 
10.23 332 
10.23 303 

9.93 643 
9.93 636 
9.93 628 
9.93 621 
9.93 614 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.70 332 
9.70 353 
9.70 375 
9.70 396 
9.70 418 

9.76 725 
9.76 754 
9.76 783 
9.76 812 
9.76 841 

10.23 275 
10.23 246 
10.23 217 
10.23 188 
10.23 159 

9.93 606 
9.93 599 
9.93 591 
9.93 584 
9.93 577 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.70 439 
9.70 461 
9.70 482 
9.70 504 
9.70 525 

9.76 870 
9.76 899 
9.76 928 
9.76 957 
9.76 986 

10.23 130 
10.23 101 
10.23 072 
10.23 043 
10.23 014 

9.93 569 
9.93 562 
9.93 554 
9.93 547 
9.93 539 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.70 547 
9.70 568 
9.70 590 
9.70 611 
9.70 633 

9.77 015 
9.77 044 
9.77 073 
9.77 101 
9.77 130 

10.22 985 
10.22 956 
10.22 927 
10.22 899 
10.22 870 

9.93 532 
9.93 525 
9.93 517 
9.93 510 
9.93 502 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.70 654 
9.70 675 
9.70 697 
9.70 718 
9.70 739 

9.77 159 
9.77 188 
9.77 217 
9.77 246 
9.77 274 

10.22 841 
10.22 812 
10.22 783 
10.22 754 
10.22 726 

9.93 495 
9.93 487 
9.93 480 
9.93 472 
9.93 465 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.70 761 
9.70 782 
9.70 803 
9.70 824 
9.70 846 

9.77 303 
9.77 332 
9.77 361 
9.77 390 
9.77 418 

10.22 697 
10.22 668 
10.22 639 
10.22 610 
10.22 582 

9.93 457 
9.93 450 
9.93 442 
9.93 435 
9.93 427 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.70 867 
9.70 888 
9.70 909 
9.70 931 
9.70 952 

9.77 447 
9.77 476 
9.77 505 
9.77 533 
9.77 562 

10.22 553 
10.22 524 
10.22 495 
10.22 467 
10.22 438 

9.93 420 
9.93 412 
9.93 405 
9.93 397 
9.93 390 

15 

14 

13 

12 

11 

60 

51 

52 

53 

54 

9.70 973 

9.70 994 

9.71 015 
9.71 036 
9.71 058 

9.77 591 
9.77 619 
9.77 648 
9.77 677 
9.77 706 

10.22 409 
10.22 381 
10.22 352 
10.22 323 
10.22 294 

9.93 382 
9.93 375 
9.93 367 
9.93 360 
9.93 352 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

60 

9.71 079 
9.71 100 
9.71 121 
9.71 142 
9.71 163 

9.77 734 
9.77 763 
9.77 791 
9.77 820 
9.77 849 

10.22 266 
10.22 237 

10.22 209 
10.22 180 

10.22 151 

9.93 344 
9.93 337 
9.93 329 
9.93 322 
9.93 314 

5 

4 

3 

2 

1 

9.71 184 

9.77 877 

10.22 123 

9.93 307 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin d 


Prop. Pts. 


59 











































































58 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


31 ° 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

9.71 184 


9.77 877 


10.22 123 

9.93 307 


60 




1 

9.71 205 

21 

9.77 906 

29 

10.22 094 

9.93 299 

8 

59 




2 

9.71 226 

21 

9.77 935 

29 

10.22 065 

9.93 291 

8 

58 




3 

9.71 247 

21 

9.77 963 

28 

10.22 037 

9.93 284 

7 

57 




4 

9.71 268 

21 

9.77 992 

29 

10.22 008 

9.93 276 

8 

56 








28 








5 

9.71 289 

ZTL 

9.78 020 

10.21 980 

9.93 269 


55 




6 

9.71 310 

21 

9.78 049 

29 

10.21 951 

9.93 261 

8 

54 




7 

9.71 331 

21 

9.78 077 

28 

10.21 923 

9.93 253 

8 

53 

,, 

29 

28 

8 

9.71 352 

21 

9.78 106 

29 

10.21 894 

9.93 246 

7 

52 




9 

9.71 373 

21 

9.78 135 

29 

10.21 865 

9.93 238 

8 

51 

6 

2.9 

2.8 





28 






3.4 
3 9 

3.3 

3 7 

10 

9.71 393 


9.78 163 

10.21 837 

9.93 230 

° 

50 

7 

g 

11 

9.71 414 

21 

9.78 192 

29 

10.21 808 

9.93 223 

7 

49 

9 

4.4 

4!2 

12 

9.71 435 

21 

9.78 220 

28 

10.21 780 

9.93 215 

8 

48 

10 

4.8 

4.7 

13 

9.71 456 

21 

9.78 249 

29 

10.21 751 

9.93 207 

8 

47 

20 

9.7 

9.3 

14 

9.71 477 

21 

21 

9.78 277 

28 

29 

10.21 723 

9.93 200 

7 

g 

46 

30 

40 

14.5 
19 3 

14.0 

18 7 

15 

9.71 498 

9.78 306 

10.21 694 

9.93 192 


45 

50 

24.2 

23.3 

16 

9.71 519 

21 

9.78 334 

28 

10.21 666 

9.93 184 

8 

44 




17 

9.71 539 

20 

9.78 363 

29 

10.21 637 

9.93 177 

7 

43 




18 

9.71 560 

21 

9.78 391 

28 

10.21 609 

9.93 169 

8 

42 




19 

9.71 581 

21 

21 

9.78 419 

28 

10.21 581 

9.93 161 

8 

7 

41 




20 

9.71 602 

9.78 448 


10.21 552 

9.93 154 

i 

40 




21 

9.71 622 

20 

9.78 476 

28 

10.21 524 

9.93 146 

8 

39 




22 

9.71 643 

21 

9.78 505 

29 

10.21 495 

9.93 138 

8 

38 




23 

9.71 664 

21 

9.78 533 

28 

10.21 467 

9.93 131 

7 

37 




24 

9.71 685 

21 

20 

9.78 562 

29 

28 

10.21 438 

9.93 123 

8 

g 

36 




25 

9.71 705 

9.78 590 

10.21 410 

9.93 115 


35 




26 

9.71 726 

21 

9.78 618 

28 

10.21 382 

9.93 108 

7 

34 

n 

21 

20 

27 

9.71 747 

21 

9.78 647 

29 

10.21 353 

9.93 100 

8 

33 




28 

9.71 767 

20 

9.78 675 

28 

10.21 325 

9.93 092 

8 

32 

6 

2.1 

2.0 

29 

9.71 788 

21 

21 

9.78 704 

29 

28 

10.21 296 

9.93 084 

8 

7 

31 

7 

8 

2.4 
2 8 

2.3 

2 7 

30 

9.71 809 

9.78 732 

10.21 268 

9.93 077 


30 

9 

3.2 

3.0 

31 

9.71 829 

20 

9.78 760 

28 

10.21 240 

9.93 069 

8 

29 

10 

3.5 

3.3 

32 

9.71 850 

21 

9.78 789 

29 

10.21 211 

9.93 061 

8 

28 

20 

7.0 

6.7 

33 

9.71 870 

20 

9.78 817 

28 

10.21 183 

9.93 053 

8 

27 

30 

40 

10.5 

14 0 

10.0 

34 

9.71 891 

21 

20 

9.78 845 

28 

29 

10.21 155 

9.93 046 

7 

g 

26 

‘±U 

50 

17.5 

10.0 

16.7 

35 

9.71 911 

9.78 874 

10.21 126 

9.93 038 


25 




36 

9.71 932 

21 

9.78 902 

28 

10.21 098 

9.93 030 

8 

21 




37 

9.71 952 

20 

9.78 930 

28 

10.21 070 

9.93 022 

8 

23 




38 

9.71 973 

21 

9.78 959 

29 

10.21 041 

9.93 014 

8 

22 




39 

9.71 994 

21 

20 

9.78 987 

28 

28 

10.21 013 

9.93 007 

7 

Q 

21 




40 

9.72 014 

9.79 015 

10.20 985 

9.92 999 

O 

20 




41 

9.72 034 

20 

9.79 043 

28 

10.20 957 

9.92 991 

8 

19 




42 

9.72 055 

21 

9.79 072 

29 

10.20 928 

9.92 983 

8 

18 




43 

9.72 075 

20 

9.79 100 

28 

10.20 900 

9.92 976 

7 

17 




44 

9.72 096 

21 

on 

9.79 128 

28 

28 

10.20 872 

9.92 968 

8 

8 

16 




45 

9.72 116 


9.79 156 

10.20 844 

9.92 960 

15 


8 

7 

46 

9.72 137 

21 

9.79 185 

29 

10.20 815 

9.92 952 

8 

14 




47 

9.72 157 

20 

9.79 213 

28 

10.20 787 

9.92 944 

8 

13 

e 

i 0.8 

0.7 

48 

9.72 177 

20 

9.79 241 

28 

10.20 759 

9.92 936 

8 

12 

7 

Q 

' 0.9 

1 1 

0.8 

O Q 

49 

9.72 198 

21 

20 

9.79 269 

28 

28 

10.20 731 

9.92 929 

7 

o 

11 

O 

9 

I 1.1 

1 1.2 

1.0 

60 

9.72 218 

9.79 297 

10.20 703 

9.92 921 

o 

10 

10 

• 1.3 

1.2 

51 

9.72 238 

20 

9.79 326 

29 

10.20 674 

9.92 913 

8 

9 

20 

30 

1 2.7 

1 d n 

2.3 

3.5 

52 

9.72 259 

21 

9.79 354 

28 

10.20 646 

9.92 905 

8 

8 

40 

' ‘±.\j 

5.3 

4!7 

53 

9.72 279 

20 

9.79 382 

28 

10.20 618 

9.92 897 

8 

7 

50 

6.7 

5.8 

54 

9.72 299 

20 

21 

9.79 410 

28 

28 

10.20 590 

9.92 889 

8 

g 

6 




55 

9.72 320 

9.79 438 

10.20 562 

9.92 881 


5 




56 

9.72 340 

20 

9.79 466 

28 

10.20 534 

9.92 874 

7 

4 




57 

9.72 360 

20 

9.79 495 

29 

10.20 505 

9.92 866 

8 

3 




58 

9.72 381 

21 

9.79 523 

28 

10.20 477 

9.92 858 

8 

2 




59 

9.72 401 

D O 

N 

9.79 551 

28 

28 

10.20 449 

9.92 850 

8 

u 

1 




60 

9.72 421 

9.79 579 

10.20 421 

9.92 842 

o 

0 





L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 


Prop. Pts. 


58 ‘ 








































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


59 


32 ° 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

0 

9.72 421 

20 

9.79 579 

28 

10.20 421 

9.92 

842 

1 

9.72 441 

9.79 607 

10.20 393 

9.92 

834 

2 

9.72 461 

20 

9.79 635 

28 

10.20 365 

9.92 

826 

3 

9.72 482 

21 

9.79 663 

28 

10.20 337 

9.92 

818 

4 

9.72 502 

20 

20 

9.79 691 

28 

28 

10.20 309 

9.92 

810 

5 

9.72 522 

9.79 719 

10.20 281 

9.92 

803 

6 

9.72 542 

20 

9.79 747 

28 

10.20 253 

9.92 

795 

7 

9.72 562 

20 

9.79 776 

29 

10.20 224 

9.92 

787 

8 

9.72 582 

20 

9.79 804 

28 

10.20 196 

9.92 

779 

9 

9.72 602 

20 

20 

9.79 832 

28 

28 

10.20 168 

9.92 

771 

10 

9.72 622 

9.79 860 

10.20 140 

9.92 

763 

11 

9.72 643 

21 

9.79 888 

28 

10.20 112 

9.92 

755 

12 

9.72 663 

20 

9.79 916 

28 

10.20 084 

9.92 

747 

13 

9.72 683 

20 

9.79 944 

28 

10.20 056 

9.92 

739 

14 

9.72 703 

20 

20 

9.79 972 

28 

28 

10.20 028 

9.92 

731 

15 

9.72 723 

9.80 000 

10.20 000 

9.92 

723 

16 

9.72 743 

20 

9.80 028 

28 

10.19 972 

9.92 

715 

17 

9.72 763 

20 

9.80 056 

28 

10.19 944 

9.92 

707 

18 

9.72 783 

20 

9.80 084 

28 

10.19 916 

9.92 

699 

19 

9.72 803 

20 

20 

9.80 112 

28 

28 

10.19 888 

9.92 

691 

20 

9.72 823 

9.80 140 

10.19 860 

9.92 

683 

21 

9.72 843 

20 

9.80 168 

28 

10.19 832 

9.92 

675 

22 

9.72 863 

20 

9.80 195 

27 

10.19 805 

9.92 

667 

23 

9.72 883 

20 

9.80 223 

28 

10.19 777 

9.92 

659 

24 

9.72 902 

19 

20 

9.80 251 

28 

28 

10.19 749 

9.92 

651 

25 

9.72 922 

9.80 279 

10.19 721 

9.92 

643 

26 

9.72 942 

20 

9.80 307 

28 

10.19 693 

9.92 

635 

27 

9.72 962 

20 

9.80 335 

28 

10.19 665 

9.92 

627 

28 

9.72 982 

20 

9.80 363 

28 

10.19 637 

9.92 

619 

29 

9.73 002 

20 

20 

9.80 391 

28 

10.19 609 

9.92 

611 

30 

9.73 022 

9.80 419 

28 

10.19 581 

9.92 

603 

31 

9.73 041 

19 

9.80 447 

10.19 553 

9.92 

595 

32 

9.73 061 

20 

9.80 474 

27 

10.19 526 

9.92 

587 

33 

9.73 081 

20 

9.80 502 

28 

10.19 498 

9.92 

579 

34 

9.73 101 

20 

20 

9.80 530 

28 

98 

10.19 470 

9.92 

571 

35 

9.73 121 

9.80 558 

AO 

28 

10.19 442 

9.92 

563 

36 

9.73 140 

19 

9.80 586 

10.19 414 

9.92 

555 

37 

9.73 160 

20 

9.80 614 

28 

10.19 386 

9.92 

546 

38 

9.73 180 

20 

9.80 642 

28 

10.19 358 

9.92 

538 

39 

9.73 200 

20 

19 

9.80 669 

27 

98 

10.19 331 

9.92 

530 

40 

9.73 219 

9.80 697 

AO 

28 

10.19 303 

9.92 

522 

41 

9.73 239 

20 

9.80 725 

10.19 275 

9.92 

514 

42 

9.73 259 

20 

9.80 753 

28 

10.19 247 

9.92 

506 

43 

9.73 278 

19 

9.80 781 

28 

10.19 219 

9.92 

498 

44 

9.73 298 

20 

OA 

9.80 808 

27 

98 

10.19 192 

9.92 

490 

45 

9.73 318 

Zi) 

9.80 836 

AO 

10.19 164 

9.92 

482 

46 

9.73 337 

19 

9.80 864 

28 

10.19 136 

9.92 

473 

47 

9.73 357 

20 

9.80 892 

28 

10.19 108 

9.92 

465 

48 

9.73 377 

20 

9.80 919 

27 

10.19 081 

9.92 

457 

49 

9.73 396 

19 

OA 

9.80 947 

28 

98 

10.19 053 

9.92 

449 

60 

9.73 416 


9.80 975 

AO 

28 

10.19 025 

9.92 

441 

51 

9.73 435 

19 

9.81 003 

10.18 997 

9.92 

433 

52 

9.73 455 

20 

9.81 030 

2 7 

10.18 970 

9.92 

425 

53 

9.73 474 

19 

9.81 058 

28 

10.18 942 

9.92 

416 

54 

9.73 494 

20 

1 A 

9.81 086 

28 

97 

10.18 914 

9.92 

408 

55 

9.73 513 

ly 

9.81 113 

28 

10.18 887 

9.92 

400 

56 

9.73 533 

20 

9.81 141 

10.18 859 

9.92 

392 

57 

9.73 552 

19 

9.81 169 

28 

10.18 831 

9.92 

384 

58 

9.73 572 

20 

9.81 196 

27 

10.18 804 

9.92 

376 

59 

9.73 591 

19 

O A 

9.81 224 

28 

98 

10.18 776 

9.92 

367 

60 

9.73 611 

Z\) 

9.81 252 

AO 

10.18 748 

9.92 

359 


1/ Oos 

d 

L Cot 

c d 

L Tan 

L Sin 


Prop. Pts. 



29 

28 

27 

6 

2.9 

2.8 

2.7 

7 

3.5 

3.3 

3.2 

8 

3.9 

3.7 

3.6 

9 

4.4 

4.2 

4.0 

10 

4.8 

4.7 

4.5 

20 

9.7 

9.3 

9.0 

30 

14.5 

14.0 

13.5 

40 

19.3 

18.7 

18.0 

50 

24.2 

23.3 

22.5 


" 

21 

20 

19 

6 

2.1 

2.0 

1.9 

7 

2.4 

2.3 

2.2 

8 

2.8 

2.7 

2.5 

9 

3.2 

3.0 

2.8 

10 

3.5 

3.3 

3.2 

20 

7.0 

6.7 

6.3 

30 

10.5 

10.0 

9.5 

40 

14.0 

13.3 

12.7 

50 

17.5 

16.7 

15.8 


" 

9 

8 

6 

0.9 

0.8 

7 

1.0 

0.9 

8 

1.2 

1.1 

9 

1.4 

1.2 

10 

1.5 

1.3 

20 

3.0 

2.7 

30 

4.5 

4.0 

40 

6.0 

5.3 

50 

7.5 

6.7 


Prop. Pts. 


57 ' 
















































































60 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


33 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.73 611 
9.73 630 
9.73 650 
9.73 669 
9.73 689 

19 

20 

19 

20 
19 

19 

20 
19 

19 

20 

19 

19 

20 
19 

19 

20 
19 
19 
19 

19 

20 
19 
19 
19 

19 

20 
19 
19 
19 
19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

19 

18 

19 

19 

19 

19 

19 

18 

19 

19 

19 

18 

19 

9.81 252 
9.81 279 
9.81 307 
9.81 335 
9.81 362 

27 

28 
28 

27 

28 

28 

27 

28 

27 

28 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 

27 

28 
27 

27 

28 

27 

28 
27 

27 

28 

27 

28 
27 

27 

28 
27 

27 

28 
27 

27 

28 
27 
27 

27 

28 
27 
27 

27 

28 

10.18 748 
10.18 721 
10.18 693 
10.18 665 
10.18 638 

9.92 359 
9.92 351 
9.92 343 
9.92 335 
9.92 326 

8 

8 

8 

9 

8 

8 

8 

9 

8 

8 

8 

9 

8 

8 

9 

8 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

8 

9 

8 

9 

8 

8 

9 

8 

9 

8 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

60 

59 

58 

57 

56 

” 28 27 20 

6 2.8 2.7 2.0 

7 3.3 3.2 2.3 

8 3.7 3.6 2.7 

9 4.2 4.0 3.0 

10 4.7 4.5 3.3 

20 9.3 9.0 6.7 

30 14.0 13.5 10.0 

40 18.7 18.0 13.3 

50 23.3 22.5 16.7 

” 19 18 

6 1.9 1.8 

7 2.2 2.1 

8 2.5 2.4 

9 2.9 2.7 

10 3.2 3.0 

20 6.3 6.0 

30 9.5 9.0 

40 12.7 12.0 

50 15.8 15.0 

"98 

6 0.9 0.8 

7 1.0 0.9 

8 1.2 1.1 

9 1.4 1.2 

10 1.5 1.3 

20 3.0 2.7 

30 4.5 4.0 

40 6.0 5.3 

50 7.5 6.7 

5 

6 

7 

8 

9 

9.73 708 
9.73 727 
9.73 747 
9.73 766 
9.73 785 

9.81 390 
9.81 418 
9.81 445 
9.81 473 
9.81 500 

10.18 610 
10.18 582 
10.18 555 
10.18 527 
10.18 500 

9.92 318 
9.92 310 
9.92 302 
9.92 293 
9.92 285 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.73 805 
9.73 824 
9.73 843 
9.73 863 
9.73 882 

9.81 528 
9.81 556 
9.81 583 
9.81 611 
9.81,638 

10.18 472 
10.18 444 
10.18 417 
10.18 389 
10.18 362 

9.92 277 
9.92 269 
9.92 260 
9.92 252 
9.92 244 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.73 901 
9.73 921 
9.73 940 
9.73 959 
9.73 978 

9.81 666 
9.81 693 
9.81 721 
9.81 748 
9.81 776 

10.18 334 
10.18 307 
10.18 279 
10.18 252 
10.18 224 

9.92 235 
9.92 227 
9.92 219 
9.92 211 
9.92 202 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.73 997 

9.74 017 
9.74 036 
9.74 055 
9.74 074 

9.81 803 
9.81 831 
9.81 858 
9.81 886 
9.81 913 

10.18 197 
10.18 169 
10.18 142 
10.18 114 
10.18 087 

9.92 194 
9.92 186 
9.92 177 
9.92 169 
9.92 161 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.74 093 
9.74 113 
9.74 132 
9.74 151 
9.74 170 

9.81 941 
9.81 968 

9.81 996 

9.82 023 
9.82 051 

10.18 059 
10.18 032 
10.18 004 
10.17 977 
10.17 949 

9.92 152 
9.92 144 
9.92 136 
9.92 127 
9.92 119 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.74 189 
9.74 208 
9.74 227 
9.74 246 
9.74 265 

9.82 078 
9.82 106 
9.82 1.33 
9.82 161 
9.82 188 

10.17 922 
10.17 894 
10.17 867 
10.17 839 
10.17 812 

9.92 111 
9.92 102 
9.92 094 
9.92 086 
9.92 077 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.74 284 
9.74 303 
9.74 322 
9.74 341 
9.74 360 

9.82 215 
9.82 243 
9.82 270 
9.82 298 
9.82 325 

10.17 785 
10.17 757 
10.17 730 
10.17 702 
10.17 675 

9.92 069 
9.92 060 
9.92 052 
9.92 044 
9.92 035 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.74 379 
9.74 398 
9.74 417 
9.74 436 
9.74 455 

9.82 352 
9.82 380 
9.82 407 
9.82 435 
9.82 462 

10.17 648 
10.17 620 
10.17 593 
10.17 565 
10.17 538 

9.92 027 
9.92 018 
9.92 010 
9.92 002 
9.91 993 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.74 474 
9.74 493 
9.74 512 
9.74 531 
9.74 549 

9.82 489 
9.82 517 
9.82 544 
9.82 571 
9.82 599 

10.17 511 
10.17 483 
10.17 456 
10.17 429 
10.17 401 

9.91 985 
9.91 976 
9.91 968 
9.91 959 
9.91 951 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.74 568 
9.74 587 
9.74 606 
9.74 625 
9.74 644 

9.82 626 
9.82 653 
9.82 681 
9.82 708 
9.82 735 

10.17 374 
10.17 347 
10.17 319 
10.17 292 
10.17 265 

9.91 942 
9.91 934 
9.91 925 
9.91 917 
9.91 908 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.74 662 
9.74 681 
9.74 700 
9.74 719 
9.74 737 

9.82 762 
9.82 790 
9.82 817 
9.82 844 
9.82 871 

10.17 238 
10.17 210 
10.17 183 
10.17 156 
10.17 129 

9.91 900 
9.91 891 
9.91 883 
9.91 874 
9.91 866 

5 

4 

3 

2 

1 

60 

9.74 756 

9.82 899 

10.17 101 

9.91 857 

0 


L Cos d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


56 ' 









































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


61 


34 ° 



L Sin 

d 

L Xd.n 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.74 756 
9.74 775 
9.74 794 
9.74 812 
9.74 831 

19 

19 

18 

19 

19 

18 

19 

19 

18 

19 

18 

19 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

19 

18 

18 

19 

18 

19 

18 

18 

19 

18 

18 

18 

19 

18 

18 

19 

18 

18 

18 

18 

19 

18 

18 

18 

18 

18 

19 

18 

18 

18 

18 

18 

18 

- 18 

9.82 899 
9.82 926 
9.82 953 

9.82 980 

9.83 008 

27 

27 

27 

28 

27 

27 

27 

28 
27 
27 

27 

27 

27 

28 
27 

27 

27 

27 

27 

27 

28 
27 
27 
27 
27 

27 

27 

27 

27 

27 

27 

28 
27 
27 
27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

27 

26 
27 
27 
27 
■ 27 

27 
27 
27 
27 
- 27 

10.17 101 
10.17 074 
10.17 047 
10.17 020 
10.16 992 

9.91 857 
9.91 849 
9.91 840 
9.91 832 
9.91 823 

8 

9 

8 

9 

8 

9 

8 

9 

8 

9 

9 

8 

9 

8 

9 

9 

8 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

8 

9 

9 

9 

8 

9 

9 

8 

9 

9 

9 

8 

9 

9 

9 

9 

8 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 

60 

59 

58 

57 

56 

" 28 27 26 

6 2.8 2.7 2.6 

7 3.3 3.2 3.0 

8 3.7 3.6 3.5 

9 4.2 4.0 3.9 

10 4.7 4.5 4.3 

20 9.3 9.0 8.7 

30 14.0 13.5 13.0 

40 18.7 18.0 17.3 

50 23.3 22.5 21.7 

" 19 18 

6 1.9 1.8 

7 2.2 2.1 

8 2.5 2.4 

9 2.8 2.7 

10 3.2 3.0 

20 6.3 6.0 

30 9.5 9.0 

40 12.7 12.0 

50 15.8 15.0 

"98 

6 0.9 0.8 

7 1.0 0.9 

8 1.2 1.1 

9 1.4 1.2 

10 1.5 1.3 

20 3.0 2.7 

30 4.5 4.0 

40 6.0 5.3 

50 7.5 6.7 

5 

6 

7 

8 

9 

9.74 850 
9.74 868 
9.74 887 
9.74 906 
9.74 924 

9.83 035 
9.83 062 
9.83 089 
9.83 117 
9.83 144 

10.16 965 
10.16 938 
10.16 911 
10.16 883 
10.16 856 

9.91 815 
9.91 806 
9.91 798 
9.91 789 
9.91 781 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.74 943 
9.74 961 
9.74 980 

9.74 999 

9.75 017 

9.83 171 
9.83 198 
9.83 225 
9.83 252 
9.83 280 

10.16 829 
10.16 802 
10.16 775 
10.16 748 
10.16 720 

9.91 772 
9.91 763 
9.91 755 
9.91 746 
9.91 738 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.75 036 
9.75 054 
9.75 073 
9.75 091 
9.75 110 

9.83 307 
9.83 334 
9.83 361 
9.83 388 
9.83 415 

10.16 693 
10.16 666 
10.16 639 
10.16 612 
10.16 585 

9.91 729 
9.91 720 
9.91 712 
9.91 703 
9.91 695 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.75 128 
9.75 147 
9.75 165 
9.75 184 
9.75 202 

9.83 442 
9.83 470 
9.83 497 
9.83 524 
9.83 551 

10.16 558 
10.16 530 
10.16 503 
10.16 476 
10.16 449 

9.91 686 
9.91 677 
9.91 669 
9.91 660 
9.91 651 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.75 221 
9.75 239 
9.75 258 
9.75 276 
9.75 294 

9.83 578 
9.83 605 
9.83 632 
9.83 659 
9.83 686 

10.16 422 
10.16 395 
10.16 368 
10.16 341 
10.16 314 

9.91 643 
9.91 634 
9.91 625 
9.91 617 
9.91 608 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.75 313 
9.75 331 
9.75 350 
9.75 368 
9.75 386 

9.83 713 
9.83 740 
9.83 768 
9.83 795 
9.83 822 

10.16 287 
10.16 260 
10.16 232 
10.16 205 
10.16 178 

9.91 599 
9.91 591 
9.91 582 
9.91 573 
9.91 565 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.75 405 
9.75 423 
9.75 441 
9.75 459 
9.75 478 

9.83 849 
9.83 876 
9.83 903 
9.83 930 
9.83 957 

10.16 151 
10.16 124 
10.16 097 
10.16 070 
10.16 043 

9.91 556 
9.91 547 
9.91 538 
9.91 530 
9.91 521 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.75 496 
9.75 514 
9.75 533 
9.75 551 
9.75 569 

9.83 984 

9.84 on 
9.84 038 
9.84 065 
9.84 092 

10.16 016 
10.15 989 
10.15 962 
10.15 935 
10.15 908 

9.91 512 
9.91 504 
9.91 495 
9.91 486 
9.91 477 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.75 587 
9.75 605 
9.75 624 
9.75 642 
9.75 660 

9.84 119 
9.84 146 
9.84 173 
9.84 200 
9.84 227 

10.15 881 
10.15 854 
10.15 827 
10.15 800 
10.15 773 

9.91 469 
9.91 460 
9.91 451 
9.91 442 
9.91 433 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.75 678 
9.75 696 
9.75 714 
9.75 733 
9.75 751 

9.84 254 
9.84 280 
9.84 307 
9.84 334 
9.84 361 

10.15 746 
10.15 720 
10.15 693 
10.15 666 
10.15 639 

9.91 425 
9.91 416 
9.91 407 
9.91 398 
9.91 389 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.75 769 
9.75 787 
9.75 805 
9.75 823 
9.75 841 

9.84 388 
9.84 415 
9.84 442 
9.84 469 
9.84 496 

10.15 612 
10.15 585 
10.15 558 
10.15 531 
10.15 504 

9.91 381 
9.91 372 
9.91 363 
9.91 354 
9.91 345 

5 

4 

3 

2 

1 


60 

9.75 859 

9.84 523 

10.15 477 

9.91 336 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


55 ° 




























































































62 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


35 ° 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.75 859 
9.75 877 
9.75 895 
9.75 913 
9.75 931 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

18 

17 

18 
18 
18 
18 

18 

17 

18 
18 
18 

17 

18 
18 
18 

17 

18 
18 

17 

18 
18 

17 

18 
18 

17 

18 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 

17 

18 
17 

17 

18 

9.84 523 
9.84 550 
9.84 576 
9.84 603 
9.84 630 

27 

26 

27 

27 

27 

27 

27 

27 

26 

27 

27 

27 

27 

27 

26 

27 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

27 

26 

27 

26 

27 

27 

26 

27 

26 

27 

27 

26 

10.15 477 
10.15 450 
10.15 424 
10.15 397 
10.15 370 

9.91 336 
9.91 328 
9.91 319 
9.91 310 
9.91 301 

8 

9 

9 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

8 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

10 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

9 

10 

9 

9 

9 

9 

9 

9 

10 

9 

9 

9 

9 

60 

59 

58 

57 

56 

" 27 26 18 

6 2.7 2.6 1.8 

7 3.2 3.0 2.1 

8 3.6 3.5 2.4 

9 4.0 3.9 2.7 

10 4.5 4.3 3.0 

20 9.0 8.7 6.0 

30 13.5 13.0 9.0 

40 18.0 17.3 12.0 

50 22.5 21.7 15.0 

" 17 10 

6 1.7 1.0 

7 2.0 1.2 

8 2.3 1.3 

9 2.6 1.5 

10 2.8 1.7 

20 5.7 3.3 

30 8.5 5.0 

40 11.3 6.7 

50 14.2 8.3 

"98 

6 0.9 0.8 

7 1.0 0.9 

8 1.2 1.1 

9 1.4 1.2 

10 1.5 1.3 

20 3.0 2.7 

30 4.5 4.0 

40 6.0 5.3 

50 7.5 6.7 

5 

6 

7 

8 

9 

9.75 949 
9.75 967 

9.75 985 

9.76 003 
9.76 021 

9.84 657 
9.84 684 
9.84 711 
9.84 738 
9.84 764 

10.15 343 
10.15 316 
10.15 289 
10.15 262 
10.15 236 

9.91 292 
9.91 283 
9.91 274 

9.91 266 

9.91 257 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.76 039 
9.76 057 
9.76 075 
9.76 093 
9.76 111 

9.84 791 
9.84 818 
9.84 845 
9.84 872 
9.84 899 

10.15 209 
10.15 182 
10.15 155 
10.15 128 
10.15 101 

9.91 248 
9.91 239 
9.91 230 
9.91 221 
9.91 212 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.76 129 
9.76 146 
9.76 164 
9.76 182 
9.76 200 

9.84 925 
9.84 952 

9.84 979 

9.85 006 
9.85 033 

10.15 075 
10.15 048 
10.15 021 
10.14 994 
10.14 967 

9.91 203 
9.91 194 
9.91 185 
9.91 176 
9.91 167 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.76 218 
9.76 236 
9.76 253 
9.76 271 
9.76 289 

9.85 059 
9.85 086 
9.85 113 
9.85 140 
9.85 166 

10.14 941 
10.14 914 
10.14 887 
10.14 860 
10.14 834 

9.91 158 
9.91 149 
9.91 141 
9.91 132 
9.91 123 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.76 307 
9.76 324 
9.76 342 
9.76 360 
9.76 378 

9.85 193 
9.85 220 
9.85 247 
9.85 273 
9.85 300 

10.14 807 
10.14 780 
10.14 753 
10.14 727 
10.14 700 

9.91 114 
9.91 105 
9.91 096 
9.91 087 
9.91 078 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.76 395 
9.76 413 
9.76 431 
9.76 448 
9.76 466 

9.85 327 
9.85 354 
9.85 380 
9.85 407 
9.85 434 

10.14 673 
10.14 646 
10.14 620 
10.14 593 
10.14 566 

9.91 069 
9.91 060 
9.91 051 
9.91 042 
9.91 033 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.76 484 
9.76 501 
9.76 519 
9.76 537 
9.76 554 

9.85 460 
9.85 487 
9.85 514 
9.85 540 
9.85 567 

10.14 540 
10.14 513 
10.14 486 
10.14 460 
10.14 433 

9.91 023 
9.91 014 
9.91 005 
9.90 996 
9.90 987 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.76 572 
9.76 590 
9.76 607 
9.76 625 
9.76 642 

9.85 594 
9.85 620 
9.85 647 
9.85 674 
9.85 700 

10.14 406 
10.14 380 
10.14 353 
10.14 326 
10.14 300 

9.90 978 
9.90 969 
9.90 960 
9.90 951 
9.90 942 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.76 660 
9.76 677 
9.76 695 
9.76 712 
9.76 730 

9.85 727 
9.85 754 
9.85 780 
9.85 807 
9.85 834 

10.14 273 
10.14 246 
10.14 220 
10.14 193 
10.14 166 

9.90 933 
9.90 924 
9.90 915 
9.90 906 
9.90 896 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.76 747 
9.76 765 
9.76 782 
9.76 800 
9.76 817 

9.85 860 
9.85 887 
9.85 913 
9.85 940 
9.85 967 

10.14 140 
10.14 113 
10.14 087 
10.14 060 
10.14 033 

9.90 887 
9.90 878 
9.90 869 
9.90 860 
9.90 851 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.76 835 
9.76 852 
9.76 870 
9.76 887 
9.76 904 

9.85 993 

9.86 020 
9.86 046 
9.86 073 
9.86 100 

10.14 007 
10.13 980 
10.13 954 
10.13 927 
10.13 900 

9.90 842 
9.90 832 
9.90 823 
9.90 814 
9.90 805 

5 

4 

3 

2 

1 

60 

9.76 922 

9.86 126 

10.13 874 

9.90 796 

0 


L Cos 

d 

LCot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


54 * 









































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


63 


36 ° 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.76 922 
9.76 939 
9.76 957 
9.76 974 
9.76 991 

17 

18 
17 

17 

18 

17 

17 

18 
17 
17 

17 

18 
17 
17 

17 

18 
17 
17 

17 

18 

17 

17 

17 

17 

17 

17 

17 

18 
17 
17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

17 

16 

17 

17 

17 

17 

17 

17 

16 

17 

17 

17 

17 

16 

9.86 126 
9.86 153 
9.86 179 
9.86 206 
9.86 232 

27 

26 

27 

26 

27 

26 

27 

26 

27 

27 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

27 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

27 

26 

27 

26 

26 

27 

26 

26 

27 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

27 

26 

26 

26 

10.13 874 
10.13 847 
10.13 821 
10.13 794 
10.13 768 

9.90 796 
9.90 787 
9.90 777 
9.90 768 
9.90 759 

9 

10 

9 

9 

9 

9 

10 

9 

9 

9 

10 

9 

9 

9 

10 

9 

9 

9 

10 

9 

9 

10 

9 

9 

9 

10 

9 

9 

10 

9 

9 

10 

9 

10 

9 

9 

10 

9 

9 

10 

. 9 
10 

9 

10 

9 

9 

10 

9 

10 

9 

10 

9 

10 

9 

10 

9 

10 

9 

10 

9 

60 

59 

58 

57 

56 

" 27 26 18 

6 2.7 2.6 1.8 

7 3.2 3.0 2.1 

8 3.6 3.5 2.4 

9 4.0 3.9 2.7 

10 4.5 4.3 3.0 

20 9.0 8.7 6.0 

30 13.5 13.0 9.0 

40 18.0 17.3 12.0 

50 22.5 21.7 15.0 

" 17 16 

6 1.7 1.6 

7 2.0 1.9 

8 2.3 2.1 

9 2.6 2.4 

10 2.8 2.7 

20 5.7 5.3 

30 8.5 8.0 

40 11.3 10.7 

50 14.2 13.3 

" 10 9 

6 1.0 0.9 

7 1.2 1.0 

8 1.3 1.2 

9 1.5 1.4 

10 1.7 1.5 

20 3.3 3.0 

30 5.0 4.5 

40 6.7 6.0 

50 8.3 7.5 

5 

6 

7 

8 

9 

9.77 009 
9.77 026 
9.77 043 
9.77 061 
9.77 078 

9.86 259 
9.86 285 
9.86 312 
9.86 338 
9.86 365 

10.13 741 
10.13 715 
10.13 688 
10.13 662 
10.13 635 

9.90 750 
9.90 741 
9.90 731 
9.90 722 
9.90 713 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.77 095 
9.77 112 
9.77 130 
9.77 147 
9.77 164 

9.86 392 
9.86 418 
9.86 445 
9.86 471 
9.86 498 

10.13 608 
10.13 582 
10.13 555 
10.13 529 
10.13 502 

9.90 704 
9.90 694 
9.90 685 
9.90 676 
9.90 667 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.77 181 
9.77 199 
9.77 216 
9.77 233 
9.77 250 

9.86 524 
9.86 551 
9.86 577 
9.86 603 
9.86 630 

10.13 476 
10.13 449 
10.13 423 
10.13 397 
10.13 370 

9.90 657 
9.90 648 
9.90 639 
9.90 630 
9.90 620 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.77 268 
9.77 285 
9.77 302 
9.77 319 
9.77-336 

9.86 656 
9.86 683 
9.86 709 
9.86 736 
9.86 762 

10.13 344 
10.13 317 
10.13 291 
10.13 264 
10.13 238 

9.90 611 
9.90 602 
9.90 592 
9.90 583 
9.90 574 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.77 353 
9.77 370 
9.77 387 
9.77 405 
9.77 422 

9.86 789 
9.86 815 
9.86 842 
9.86 868 
9.86 894 

10.13 211 
10.13 185 
10.13 158 
10.13 132 
10.13 106 

9.90 565 
9.90 555 
9.90 546 
9.90 537 
9.90 527 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.77 439 
9.77 456 
9.77 473 
9.77 490 
9.77 507 

9.86 921 
9.86 947 

9.86 974 

9.87 000 
9.87 027 

10.13 079 
10.13 053 
10.13 026 
10.13 000 
10.12 973 

9.90 518 
9.90 509 
9.90 499 
9.90 490 
9.90 480 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.77 524 
9.77 541 
9.77 558 
9.77 575 
9.77 592 

9.87 053 
9.87 079 
9.87 106 
9.87 132 
9.87 158 

10.12 947 
10.12 921 
10.12 894 
10.12 868 
10.12 842 

9.90 471 
9.90 462 
9.90 452 
9.90 443 
9.90 434 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.77 609 
9.77 626 
9.77 643 
9.77 660 
9.77 677 

9.87 185 
9.87 211 
9.87 238 
9.87 264 
9.87 290 

10.12 815 
10.12 789 
10.12 762 
10.12 736 
10.12 710 

9.90 424 
9.90 415 
9.90 405 
9.90 396 
9.90 386 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.77 694 
9.77 711 
9.77 728 
9.77 744 
9.77 761 

9.87 317 
9.87 343 
9.87 369 
9.87 396 
9.87 422 

10.12 683 
10.12 657 
10.12 631 
10.12 604 
10.12 578 

9.90 377 
9.90 368 
9.90 358 
9.90 349 
9.90 339 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.77 778 
9.77 795 
9.77 812 
9.77 829 
9.77 846 

9.87 448 
9.87 475 
9.87 501 
9.87 527 
9.87 554 

10.12 552 
10.12 525 
10.12 499 
10.12 473 
10.12 446 

9.90 330 
9.90 320 
9.90 311 
9.90 301 
9.90 292 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.77 862 
9.77 879 
9.77 896 
9.77 913 
9.77 930 

9.87 580 
9.87 606 
9.87 633 
9.87 659 
9.87 685 

10.12 420 
10.12 394 
10.12 367 
10.12 341 
10.12 315 

9.90 282 
9.90 273 
9.90 263 
9.90 254 
9.90 244 

5 

4 

3 

2 

1. 

60 

9.77 946 

9.87 711 

10.12 289 

9.90 235 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


53 














































































64 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


37 ° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

9.77 946 


9.87 711 


10.12 289 

9.90 235 


60 







1 

9.77 963 

17 

9.87 738 

27 

10.12 262 

9.90 225 

10 

59 







2 

9.77 980 

17 

9.87 764 

26 

10.12 236 

9.90 216 

9 

58 







3 

9.77 997 

17 

9.87 790 

26 

10.12 210 

9.90 206 

10 

57 







4 

9.78 013 

16 

17 

9.87 817 

27 

26 

10.12 183 

9.90 197 

9 

10 

56 







5 

9.78 030 

9.87 843 

10.12 1.57 

9.90 187 

55 







6 

9.78 047 

17 

9.87 869 

26 

10.12 131 

9.90 178 

9 

54 







7 

9.78 063 

16 

9.87 895 

26 

10.12 105 

9.90 168 

10 

53 







8 

9.78 080 

17 

9.87 922 

27 

10.12 078 

9.90 159 

9 

52 







9 

9.78 097 

17 

16 

9.87 948 

26 

26 

10.12 052 

9.90 149 

10 

10 

51 







10 

9.78 113 

9.87 974 

10.12 026 

9.90 139 

50 







11 

9.78 130 

17 

9.88 000 

26 

10.12 000 

9.90 130 

9 

49 







12 

9.78 147 

i i 

9.88 027 

27 

10.11 973 

9.90 120 

10 

48 







13 

9.78 163 

16 

9.88 053 

26 

10.11 947 

9.90 111 

9 

47 







14 

9.78 180 

17 

17 

9.88 079 

26 

26 

10.11 921 

9.90 101 

10 

10 

46 

" 


27 


26 

17 

15 

9.78 197 

9.88 105 

10.11 895 

9.90 091 

45 

6 


2.7 


2.6 

1.7 

16 

9.78 213 

16 

9.88 131 

26 

10.11 869 

9.90 082 

9 

44 

7 


3.2 


3.0 

2.0 

17 

9.78 230 

17 

9.88 158 

27 

10.11 842 

9.90 072 

10 

43 

8 


3.6 


3.5 

2.3 

18 

9.78 246 

16 

9.88 184 

26 

10.11 816 

9.90 063 

9 

42 

9 
1 n 


4.0 

4 e; 


3.9 

4 Q 

2.6 

9 S 

19 

9.78 263 

17 

17 

9.88 210 

26 

26 

10.11 790 

9.90 053 

10 

10 

41 

lU 

20 


*±.0 

9.0 


8.7 

Z.o 

5.7 

20 

9.78 280 

9.88 236 

10.11 764 

9.90 043 

40 

30 

13.5 

13.0 

8.5 

21 

9.78 296 

16 

9.88 262 

26 

10.11 738 

9.90 034 

9 

39 

40 

18.0 

17.3 

11.3 

22 

9.78 313 

17 

9.88 289 

27 

10.11 711 

9.90 024 

10 

38 

50 

22.5 

21.7 

14.2 

23 

9.78 329 

16 

9.88 315 

26 

10.11 685 

9.90 014 

10 

37 







24 

9.78 346 

17 

16 

9.88 341 

26 

26 

10.11 659 

9.90 005 

9 

10 

36 







25 

9.78 362 

9.88 367 

10.11 633 

9.89 995 

35 







26 

9.78 379 

17 

9.88 393 

26 

10.11 607 

9.89 985 

10 

34 







27 

9.78 395 

16 

9.88 420 

27 

10.11 580 

9.89 976 

9 

33 







28 

9.78 412 

17 

9.88 446 

26 

10.11 554 

9.89 966 

10 

32 







29 

9.78 428 

16 

17 

9.88 472 

26 

26 

10.11 528 

9.89 956 

10 

9 

31 







30 

9.78 445 

9.88 498 

10.11 502 

9.89 947 

30 







31 

9.78 461 

16 

9.88 524 

26 

10.11 476 

9.89 937 

10 

29 







32 

9.78 478 

17 

9.88 550 

26 

10.11 450 

9.89 927 

10 

28 







33 

9.78 494 

16 

9.88 577 

27 

10.11 423 

9.89 918 

9 

27 







34 

9.78 510 

16 

17 

9.88 603 

26 

26 

10.11 397 

9.89 908 

10 

10 

26 







35 

9.78 527 

9.88 629 

10.11 371 

9.89 898 

25 







36 

9.78 543 

16 

9.88 655 

26 

10.11 345 

9.89 888 

10 

24 







37 

9.78 560 

17 

9.88 681 

26 

10.11 319 

9.89 879 

9 

23 







38 

9.78 576 

16 

9.88 707 

26 

10.11 293 

9.89 869 

10 

22 







39 

9.78 592 

16 

17 

9.88 733 

26 

26 

10.11 267 

9.89 859 

10 

10 

21 



16 


10 

9 

40 

9.78 609 

9.88 759 

10.11 241 

9.89 849 

20 

( 

g 

1 6 

1.0 

0 9 

41 

9.78 625 

16 

9.88 786 . 

27 

10.11 214 

9.89 840 

9 

19 


1 

i!9 

1.2 

ilo 

42 

9.78 642 

17 

9.88 812 

26 

10.11 188 

9.89 830 

10 

18 


B 

2.1 

1.3 

1.2 

43 

9.78 658 

16 

9.88 838 

26 

10.11 162 

9.89 820 

10 

17 

9 

2.4 

1.5 

1.4 

44 

9.78 674 

16 

17 

9.88 864 

26 

26 

10.11 136 

9.89 810 

10 

o 

16 

10 

20 

2.7 
5 3 

1.7 
3 3 

1.5 

3 0 

45 

9.78 691 

9.88 890 

10.11 no 

9.89 801 

y 

15 

30 

8^0 

5.0 

4.5 

46 

9.78 707 

16 

9.88 916 

26 

10.11 084 

9.89 791 

10 

14 

40 

10.7 

6.7 

6.0 

47 

9.78 723 

16 

9.88 942 

26 

10.11 058 

9.89 781 

10 

13 

50 

13.3 

8.3 

7.5 

48 

9.78 739 

16 

9.88 968 

26 

10.11 032 

9.89 771 

10 

12 







49 

9.78 756 

17 

16 

9.88 994 

26 

26 

10.11 006 

9.89 761 

10 

Q 

11 







60 

9.78 772 

9.89 020 

10.10 980 

9.89 752 

y 

10 







51 

9.78 788 

16 

9.89 046 

26 

10.10 954 

9.89 742 

10 

9 







52 

9.78 805 

17 

9.89 073 

27 

10.10 927 

9.89 732 

10 

8 







53 

9.78 821 

► 16 

9.89 099 

26 

10.10 901 

9.89 722 

10 

7 







54 

9.78 837 

16 

16 

9.89 125 

26 

26 

10.10 875 

9.89 712 

10 

10 

6 







55 

9.78 853 

9.89 151 

10.10 849 

9.89 702 

5 







56 

9.78 869 

16 

9.89 177 

26 

10.10 823 

9.89 693 

9 

4 







57 

9.78 886 

17 

9.89 203 

26 

10.10 797 

9.89 683 

10 

3 







58 

9.78 902 

16 

9.89 229 

26 

10.10 771 

9.89 673 

10 

2 







59 

9.78 918 

16 

1 A 

9.89 255 

26 

26 

10.10 745 

9.89 663 

10 

10 

1 







60 

9.78 934 

1D 

9.89 281 

10.10 719 

9.89 653 

0 








L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


52 











































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


65 


38 ^ 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

9.78 934 


9.89 281 


10.10 719 

9.89 653 


60 

1 

9.78 950 


9.89 307 

26 

10.10 693 

9.89 643 

10 

59 

2 

9.78 967 


9.89 333 

26 

10.10 667 

9.89 6.33 

10 

58 

3 

9.78 983 


9.89 359 

26 

10.10 641 

9.89 624 

9 

57 

4 

9.78 999 

16 

16 

9.89 385 

26 

26 

10.10 615 

9.89 614 

10 

56 

b 

9.79 015 

9.89 411 

10.10 589 

9.89 604 

10 

55 

6 

9.79 031 

16 

9.89 437 

26 

10.10 563 

9.89 594 

10 

54 

7 

9.79 047 

16 

9.89 463 

26 

10.10 537 

9.89 584 

10 

53 

8 

9.79 063 

16 

9.89 489 

26 

10.10 511 

9.89 574 

10 

52 

9 

9.79 079 

16 

16 

9.89 515 

26 

26 

10.10 485 

9.89 564 

10 

51 

10 

9.79 095 

9.89 541 

10.10 459 

9.89 554 

10 

50 

11 

9.79 111 

16 

9.89 567 

26 

10.10 433 

9.89 544 

10 

49 

12 

9.79 128 

17 

9.89 593 

26 

10.10 407 

9.89 534 

10 

48 

13 

9.79 144 

16 

9.89 619 

26 

10.10 381 

9.89 524 

10 

47 

14 

9.79 160 

16 

16 

9.89 645 

26 

26 

10.10 355 

9.89 514 

10 

46 

15 

9.79 176 

9.89 671 

10.10 329 

9.89 504 

10 

45 

16 

9.79 192 

16 

9.89 697 

26 

10.10 303 

9.89 495 

9 

44 

17 

9.79 208 

16 

9.89 723 

26 

10.10 277 

9.89 485 

10 

43 

18 

9.79 224 

16 

9.89 749 

26 

10.10 251 

9.89 475 

10 

42 

19 

9.79 240 

16 

16 

9.89 775 

26 

26 

10.10 225 

9.89 465 

10 

41 

20 

9.79 256 

9.89 801 

10.10 199 

9.89 455 

10 

40 

21 

9.79 272 

16 

9.89 827 

26 

10.10 173 

9.89 445 

10 

39 

22 

9.79 288 

16 

9.89 853 

26 

10.10 147 

9.89 435 

10 

38 

23 

9.79 304 

16 

9.89 879 

26 

10.10 121 

9.89 425 

10 

37 

24 

9.79 319 

15 

16 

9.89 905 

26 

26 

10.10 095 

9.89 415 

10 

•36 

25 

9.79 335 

9.89 931 

10.10 069 

9.89 405 

10 

35 

26 

9.79 351 

16 

9.89 957 

26 

10.10 043 

9.89 395 

10 

34 

27 

9.79 367 

16 

9.89 983 

26 

10.10 017 

9.89 385 

10 

33 

28 

9.79 383 

16 

9.90 009 

26 

10.09 991 

9.89 375 

10 

32 

29 

9.79 399 

16 

16 

9.90 035 

26 

26 

10.09 965 

9.89 364 

11 

31 

30 

9.79 415 

9.90 061 

10.09 939 

9.89 354 

10 

30 

31 

9.79 431 

16 

9.90 086 

25 

10.09 914 

9.89 344 

10 

29 

32 

9.79 447 

16 

9.90 112 

26 

10.09 888 

9.89 334 

10 

28 

33 

9.79 463 

16 

9.90 138 

26 

10.09 862 

9.89 324 

10 

27 

34 

9.79 478 

15 

16 

9.90 164 

26 

26 

10.09 836 

9.89 314 

10 

26 

35 

9.79 494 

9.90 190 

10.09 810 

9.89 304 

10 

25 

36 

9.79 510 

16 

9.90 216 

26 

10.09 784 

9.89 294 

10 

24 

37 

9.79 526 

16 

9.90 242 

26 

10.09 758 

9.89 284 

10 

23 

38 

9.79 542 

16 

9.90 268 

26 

10.09 732 

9.89 274 

10 

22 

39 

9.79 558 

16 

15 

9.90 294 

26 

26 

10.09 706 

9.89 264 

10 

21 

40 

9.79 573 

9.90 320 

10.09 680 

9.89 254 

10 

20 

41 

9.79 589 

16 

9.90 346 

26 

10.09 654 

9.89 244 

10 

19 

42 

9.79 605 

16 

9.90 371 

25 

10.09 629 

9.89 233 

11 

18 

43 

9.79 621 

16 

9.90 397 

26 

10.09 603 

9.89 223 

10 

17 

44 

9.79 636 

15 

16 

9.90 423 

26 

26 

10.09 577 

9.89 213 

10 

16 

45 

9.79 652 

9.90 449 

10.09 551 

9.89 203 

10 

15 

46 

9.79 668 

16 

9.90 475 

26 

10.09 525 

9.89 193 

10 

14 

47 

9.79 684 

16 

9.90 501 

26 

10.09 499 

9.89 183 

10 

13 

48 

9.79 699 

15 

9.90 527 

26 

10.09 473 

9.89 173 

10 

12 

49 

9.79 715 

16 

16 

9.90 553 

26 

25 

10.09 447 

9.89 162 

11 

10 

11 

50 

9.79 731 

9.90 578 

10.09 422 

9.89 152 

10 

51 

9.79 746 

15 

9.90 604 

26 

10.09 396 

9.89 142 

10 

9 

52 

9.79 762 

16 

9.90 630 

26 

10.09 370 

9.89 132 

10 

8 

53 

9.79 778 

16 

9.90 656 

26 

10.09 344 

9.89 122 

10 

7 

54 

9.79 793 

15 

16 

9.90 682 

26 

26 

10.09 318 

9.89 112 

10 

11 

6 

55 

9.79 809 

9.90 708 

10.09 292 

9.89 101 

5 

56 

9.79 825 

16 

9.90 734 

26 

10.09 266 

9.89 091 

10 

4 

57 

9.79 840 

15 

9.90 759 

25 

10.09 241 

9.89 081 

10 

3 

58 

9.79 856 

16 

9.90 785 

26 

10.09 215 

9.89 071 

10 

2 

59 

9.79 872 

16 

15 

9.90 811 

26 

26 

10.09 189 

9.89 060 

11 

10 

1 

60 

9.79 887 

9.90 837 

10.09 163 

9.89 050 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 1' 


Prop. Pts. 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


16 

1.6 

1.9 

2.1 

2.4 

2.7 

5.3 

8.0 

10.7 

13.3 


Prop. Pts. 


51 












































































6G 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


39 ° 


/ 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


0 

1 

9.79 887 
9.79 903 

16 

9.90 837 
9.90 863 

26 

10.09 163 
10.09 137 

9.89 050 
9.89 040 

10 

60 

59 

2 

9.79 918 

15 

9.90 889 

26 

10.09 111 

9.89 030 

10 

58 

3 

9.79 934 

16 

9.90 914 

25 

10.09 086 

9.89 020 

10 

57 

4 

9.79 950 

16 

15 

16 

9.90 940 

26 

26 

26 

10.09 060 

9.89 009 

11 

10 

10 

56 

5 

6 

9.79 965 
9.79 981 

9.90 966 
9.90 992 

10.09 034 
10.09 008 

9.88 999 
9.88 989 

55 

54 

7 

9.79 996 

15 

9.91 018 

26 

10.08 982 

9.88 978 

11 

53 

8 

9.80 012 

16 

9.91 043 

25 

10.08 957 

9.88 968 

10 

52 

9 

9.80 027 

15 

16 

15 

9.91 069 

26 

26 

26 

10.08 931 

9.88 958 

10 

10 

11 

51 

10 

11 

9.80 043 
9.80 058 

9.91 095 
9.91 121 

10.08 905 
10.08 879 

9.88 948 
9.88 937 

50 

49 

12 

9.80 074 

16 

9.91 147 

26 

10.08 853 

9.88 927 

10 

48 

13 

9.80 089 

15 

9.91 172 

25 

10.08 828 

9.88 917 

10 

47 

14 

9.80 105 

16 

15 

16 

9.91 198 

26 

26 

26 

10.08 802 

9.88 906 

11 

10 

10 

46 

15 

16 

9.80 120 
9.80 136 

9.91 224 
9.91 250 

10.08 776 
10.08 750 

9.88 896 
9.88 886 

45 

44 

17 

9.80 151 

15 

9.91 276 

26 

10.08 724 

9.88 875 

11 

43 

18 » 

9.80 166 

15 

9.91 301 

25 

10.08 699 

9.88 865 

10 

42 

19 

9.80 182 

16 

15 

16 

9.91 327 

26 

26 

26 

10.08 673 

9.88 855 

10 

11 

10 

41 

20 

21 

9.80 197 
9.80 213 

9.91 353 
9.91 379 

10.08 647 
10.08 621 

9.88 844 
9.88 834 

40 

39 

22 

9.80 228 

15 

9.91 404 

25 

10.08 .596 

9.88 824 

10 

38 

23 

9.80 244 

16 

9.91 430 

26 

10.08 570 

9.88 813 

11 

37 

24 

9.80 259 

15 

15 

16 

9.91 456 

26 

26 

25 

10.08 544 

9.88 803 

10 

10 

11 

36 

25 

26 

9.80 274 
9.80 290 

9.91 482 
9.91 507 

10.08 518 
10.08 493 

9.88 793 
9.88 782 

35 

34 

27 

9.80 305 

15 

9.91 533 

26 

10.08 467 

9.88 772 

10 

33 

28 

9.80 320 

15 

9.91 559 

26 

10.08 441 

9.88 761 

11 

32 

29 

9.80 336 

16 

15 

15 

9.91 585 

26 

25 

26 

10.08 415 

9.88 751 

10 

10 

11 

31 

30 

31 

9.80 351 
9.80 366 

9.91 610 
9.91 636 

10.08 390 
10.08 364 

9.88 741 
9.88 730 

30 

29 

32 

9.80 382 

16 

9.91 662 

26 

10.08 338 

9.88 720 

10 

28 

33 

9.80 397 

15 

9.91 688 

26 

10.08 312 

9.88 709 

11 

27 

34 

9.80 412 

15 

16 

15 

9.91 713 

25 

26 

26 

10.08 287 

9.88 699 

10 

11 

10 

26 

35 

36 

9.80 428 
9.80 443 

9.91 739 
9.91 765 

10.08 261 
10.08 235 

9.88 688 
9.88 678 

25 

24 

37 

9.80 458 

15 

9.91 791 

26 

10.08 209 

9.88 668 

10 

23 

38 

9.80 473 

15 

9.91 816 

25 

10.08 184 

9.88 657 

11 

22 

39 

9.80 489 

16 

15 

15 

9.91 842 

26 

26 

25 

10.08 158 

9.88 647 

10 

11 

10 

21 

40 

41 

9.80 504 
9.80 519 

9.91 868 
9.91 893 

10.08 132 
10.08 107 

9.88 636 
9.88 626 

20 

19 

42 

9.80 534 

15 

9.91 919 

26 

10.08 081 

9.88 615 

11 

18 

43 

9.80 550 

16 

9.91 945 

26 

10.08 055 

9.88 605 

10 

17 

44 

9.80 565 

15 

15 

15 

9.91 971 

26 

25 

26 

10.08 029 

9.88 594 

11 

10 

11 

16 

45 

46 

9.80 580 
9.80 595 

9.91 996 

9.92 022 

10.08 004 
10.07 978 

9.88 584 
9.88 573 

15 

14 

47 

9.80 610 

15 

9.92 048 

26 

10.07 952 

9.88 563 

10 

13 

48 

9.80 625 

15 

9.92 073 

25 

10.07 927 

9.88 552 

11 

12 

49 

9.80 641 

16 

15 

15 

9.92 099 

26 

26 

25 

10.07 901 

9.88 542 

10 

11 

10 

11 

50 

51 

9.80 656 
9.80 671 

9.92 125 
9.92 150 

10.07 875 
10.07 850 

9.88 531 
9.88 521 

10 

9 

52 

9.80 686 

15 

9.92 176 

26 

10.07 824 

9.88 510 

11 

8 

53 

9.80 701 

15 

9.92 202 

26 

10.07 798 

9.88 499 

11 

7 

54 

9.80 716 

15 

15 

15 

9.92 227 

26 

26 

26 

10.07 773 

9.88 489 

10 

11 

10 

6 

55 

56 

9.80 731 
9.80 746 

9.92 253 
9.92 279 

10.07 747 
10.07 721 

9.88 478 
9.88 468 

5 

4 

57 

9.80 762 

16 

9.92 304 

25 

10.07 696 

9.88 457 

11 

3 

58 

9.80 777 

15 

9.92 330 

26 

10.07 670 

9.88 447 

10 

2 

59 

9.80 792 

15 

15 

9.92 356 

26 

25 

10.07 644 

9.88 436 

11 

11 

. 1 

60 

9.80 807 

9.92 381 

10.07 619 

9.88 425 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

t 


Prop. Pts. 


6 

7 

8 
9 

10 

20 

30 

40 

50 


26 

2.6 

3.0 

3.5 

3.9 

4.3 

8.7 

13.0 

17.3 

21.7 


25 

2.5 

2.9 

3.3 

3.8 

4.2 

8.3 
12.5 

16.7 

20.8 


6 

7 

8 
9 

10 

20 

30 

40 

50 


16 

1.6 

1.9 

2.1 

2.4 

2.7 

5.3 

8.0 

10.7 

13.3 


6 

7 

8 
9 

10 

20 

30 

40 

50 


11 

1.1 

1.3 

1.5 

1.6 
1.8 
3.7 
5.5 

7.3 
9.2 


15 

1.5 
1.8 
2.0 
2.2 

2.5 
5.0 

7.5 
10.0 
12.5 


10 

1.0 

1.2 

1.3 
1.5 

1.7 

3.3 
5.0 

6.7 

8.3 


Prop. Pts. 


50 ° 


















































































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


67 


40 ° 


/ 

L Sin 

d 

LTan 

c d 

L Cot , 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.80 807 
9.80 822 
9.80 837 
9.80 852 
9.80 867 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

15 

14 

15 
15 
15 

15 

15 

15 

15 

14 

15 
15 
15 
15 

14 

15 
15 
15 
15 

14 

15 
15 

14 

15 
15 

15 

14 

15 
15 

14 

15 
15 

14 

15 
15 

14 

15 

14 

15 
15 

14 

15 

14 

15 
14 

9.92 381 
9.92 407 
9.92 433 
9.92 458 
9.92 484 

26 

26 

25 

26 
26 

25 

26 
26 

25 

26 

25 

26 
26 

25 

26 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

26 

25 

26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 

25 

26 
26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 
25 

10.07 619 
10.07 593 
10.07 567 
10.07 542 
10.07 516 

9.88 425 
9.88 415 
9.88 404 
9.88 394 
9.88 383 

10 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

10 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

11 

11 

10 

11 

11 

11 

11 

11 

11 

11 

11 

11 

60 

59 

58 

57 

56 

" 26 25 

6 2.6 2.5 

7 3.0 2.9 

8 3.5 3.3 

9 3.9 3.8 

10 4.3 4.2 

20 8.7 8.3 

30 13.0 12.5 

40 17.3 16.7 

50 21.7 20.8 

" 15 14 

6 1.5 1.4 

7 1.8 1.6 

8 2.0 1.9 

9 2.2 2.1 

10 2.5 2.3 

20 5.0 4.7 

30 7.5 7.0 

40 10.0 9.3 

50 12.5 11.7 

" 11 10 

6 1.1 l.O 

7 1.3 1.2 

8 1.5 1.3 

9 1.6 1.5 

10 1.8 1.7 

20 3.7 3.3 

30 5.5 5.0 

40 7.3 6.7 

50 9.2.8.3 

5 

6 

7 

8 

9 

9.80 882 
9.80 897 
9.80 912 
9.80 927 
9.80 942 

9.92 510 
9.92 535 
9.92 561 
9.92 587 
9.92 612 

10.07 490 
10.07 465 
10.07 439 
10.07 413 
10.07 388 

9.88 372 
9.88 362 
9.88 351 
9.88 340 
9.88 330 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.80 957 
9.80 972 

9.80 987 

9.81 002 
9.81 017 

9.92 638 
9.92 663 
9.92 689 
9.92 715 
9.92 740 

10.07 362 
10.07 337 
10.07 311 
10.07 285 
10.07 260 

9.88 319 
9.88 308 
9.88 298 
9.88 287 
9.88 276 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.81 032 
9.81 047 
9.81 061 
9.81 076 
9.81 091 

9.92 766 
9.92 792 
9.92 817 
9.92 843 
9.92 868 

10.07 234 
10.07 208 
10.07 183 
10.07 157 
10.07 132 

9.88 266 
9.88 255 
9.88 244 
9.88 234 
9.88 223 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.81 106 
9.81 121 
9.81 136 
9.81 151 
9.81 166 

9.92 894 
9.92 920 
9.92 945 
9.92 971 
9.92 996 

10.07 106 
10.07 080 
10.07 055 
10.07 029 
10.07 004 

9.88 212 
9.88 201 
9.88 191 
9.88 180 
9.88 169 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.81 180 
9.81 195 
9.81 210 
9.81 225 
9.81 240 

9.93 022 
9.93 048 
9.93 073 
9.93 099 
9.93 124 

10.06 978 
10.06 952 
10.06 927 
10.06 901 
10.06 876 

9.88 158 
9.88 148 
9.88 137 
9.88 126 
9.88 115 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.81 254 
9.81 269 
9.81 284 
9.81 299 
9.81 314 

9.93 150 
9.93 175 
9.93 201 
9.93 227 
9.93 252 

10.06 850 
10.06 825 
10.06 799 
10.06 773 
10.06 748 

9.88 105 
9.88 094 
9.88 083 
•9.88 072 
9.88 061 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

40 

41 

42 

43 

44 

9.81 328 
9.81 343 
9.81 358 
9.81 372 
9.81 387 

9.93 278 
9.93 303 
9.93 329 
9.93 354 
9.93 380 

10.06 722 
10.06 697 
10.06 671 
10.06 646 
10.06 620 

9.88 051 
9.88 040 
9.88 029 
9.88 018 
9.88 007 

25 

24 

23 

22 

21 

9.81 402 
9.81 417 
9.81 431 
9.81 446 
9.81 461 

9.93 406 
9.93 431 
9.93 457 
9.93 482 
9.93 508 

10.06 594 
10.06 569 
10.06 543 
10.06 518 
10.06 492 

9.87 996 
9.87 985 
9.87 975 
9.87 964 
9.87 953 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.81 475 
9.81 490 
9.81 505 
9.81 519 
9.81 534 

9.93 533 
9.93 559 
9.93 584 
9.93 610 
9.93 636 

10.06 467 
10.06 441 
10.06 416 
10.06 390 
10.06 364 

9.87 942 
9.87 931 
9.87 920 
9.87 909 
9.87 898 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.81 549 
9.81 563 
9.81 578 
9.81 592 
9.81 607 

9.93 661 
9.93 687 
9.93 712 
9.93 738 
9.93 763 

10.06 339 
10.06 313 
10.06 288 
10.06 262 
10.06 237 

9.87 887 
9.87 877 
9.87 866 
9.87 855 
9.87 844 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.81 622 
9.81 636 
9.81 651 
9.81 665 
9.81 680 

9.93 789 
9.93 814 
9.93 840 
9.93 865 
9.93 891 

10.06 211 
10.06 186 
10.06 160 
10.06 135 
10.06 109 

9.87 833 
9.87 822 
9.87 811 
9.87 800 
9.87 789 

5 

4 

3 

2 

1 

60 

9.81 694 

9.93 916 

10.06 084 

9.87 778 

0 


L Cos 

d 

L Cot 

c d 

L Tan 

L Sin ! d 

' 

Prop. Pts. 


49 ' 





































































G8 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


41° 


' 

L Sin 

d 

L Tan 

cd 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.81 694 
9.81 709 
9.81 723 
9.81 738 
9.81 752 

15 

14 

15 

14 

15 

14 

15 

14 

15 

14 

15 
14 

14 

15 

14 

15 

14 

15 
14 

14 

15 
14 

14 

15 
14 

14 

15 
14 
14 

14 

15 
14 

14 

15 
14 

14 

14 

14 

15 
14 

14 

14 

14 

15 
14 

14 

14 

14 

14 

14 

14 

15 
14 
14 
14 

14 

14 

14 

14 

14 

9.93 916 
9.93 942 
9.93 967 

9.93 993 

9.94 018 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 

25 

25 

26 

25 

26 

25 

26 

25 

26 

25 

26 
25 

25 

26 

25 

26 

25 

26 
25 

25 

26 

25 

26 

25 

26 

25 

25 

26 

25 

26 

25 

26 
25 

25 

26 

10.06 084 
10.06 058 
10.06 033 
10.06 007 
10.05 982 

9.87 778 
9.87 767 
9.87 756 
9.87 745 
9.87 734 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

11 

12 

11 

11 

11 

11 

11 

11 

11 

11 

12 

11 

11 

11 

11 

11 

12 

11 

11 

11 

11 

12 

11 

11 

11 

11 

12 

11 

11 

12 

11 

11 

11 

12 

11 

11 

12 

11 

11 

12 

11 

11 

12 

11 

11 

12 

60 

59 

58 

57 

56 


5 

6 

7 

8 

9 

9.81 767 
9.81 781 
9.81 796 
9.81 810 
9.81 825 

9.94 044 
9.94 069 
9.94 095 
9.94 120 
9.94 146 

10.05 956 
10.05 931 
10.05 905 
10.05 880 
10.05 854 

9.87 723 
9.87 712 
9.87 701 
9.87 690 
9.87 679 

55 

54 

53 

52 

51 

" 26 25 

6 2.6 2.5 

7 3.0 2.9 

8 3.5 3.3 

9 3.9 3.8 

10 4.3 4.2 

20 8.7 8.3 

30 13.0 12.5 

40 17.3 16.7 

50 21.7 20.8 

" 15 14 

6 1.5 1.4 

7 1.8 1.6 

8 2.0 1.9 

9 2.2 2.1 

10 2.5 2.3 

20 5.0 4.7 

30 7.5 7.0 

40 10.0 9.3 

50 12.5 11.7 

" 12 11 

6 1.2 1.1 

7 1.4 1.3 

8 1.6 1.5 

9 1.8 1.6 

10 2.0 1.8 

20 4.0 3.7 

30 6.0 5.5 

40 8.0 7.3 

50 10.0 9.2 

10 

11 

12 

13 

14 

9.81 839 
9.81 854 
9.81 868 
9.81 882 
9.81 897 

9.94 171 
9.94 197 
9.94 222 
9.94 248 
9.94 273 

10.05 829 
10.05 803 
10.05 778 
10.05 752 
10.05 727 

9.87 668 
9.87 657 
9.87 646 
9.87 635 
9.87 624 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.81 911 
9.81 926 
9.81 940 
9.81 955 
9.81 969 

9.94 299 
9.94 324 
9.94 350 
9.94 375 
9.94 401 

10.05 701 
10.05 676 
10.05 650 
10.05 625 
10.05 599 

9.87 613 
9.87 601 
9.87 590 
9.87 579 
9.87 568 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.81 983 

9.81 998 

9.82 012 
9.82 026 
9.82 041 

9.94 426 
9.94 452 
9.94 477 
9.94 503 
9.94 528 

10.05 574 
10.05 548 
10.05 523 
10.05 497 
10.05 472 

9.87 557 
9.87 546 
9.87 535 
9.87 524 
9.87 513 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.82 055 
9.82 069 
9.82 084 
9.82 098 
9.82 112 

9.94 554 
9.94 579 
9.94 604 
9.94 630 
9.94 655 

10.05 446 
10.05 421 
10.05 396 
10.05 370 
10.05 345 

9.87 501 
9.87 490 
9.87 479 
9.87 468 
9.87 457 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.82 126 
9.82 141 
9.82 155 
9.82 169 
9.82 184 

9.94 681 
9.94 706 
9.94 732 
9.94 757 
9.94 783 

10.05 319 
10.05 294 
10.05 268 
10.05 243 
10.05 217 

9.87 446 
9.87 434 
9.87 423 
9.87 412 
9.87 401 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.82 198 
9.82 212 
9.82 226 
9.82 240 
9.82 255 

9.94 808 
9.94 834 
9.94 859 
9.94 884 
9.94 910 

10.05 192 
10.05 166 
10.05 141 
10.05 116 
10.05 090 

9.87 390 
9.87 378 
9.87 367 
9.87 356 
9.87 345 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

9.82 269 
9.82 283 
9.82 297 
9.82 311 
9.82 326 

9.94 935 
9.94 961 

9.94 986 

9.95 012 
9.95 037 

10.05 065 
10.05 039 
10.05 014 
10.04 988 
10.04 963 

9.87 334 
9.87 322 
9.87 311 
9.87 300 
9.87 288 

20 

19 

18 

17 

16 

45 

46 

47 

48 

49 

9.82 340 
9.82 354 
9.82 368 
9.82 382 
9.82 396 

9.95 062 
9.95 088 
9.95 113 
9.95 139 
9.95 164 

10.04 938 
10.04 912 
10.04 887 
10.04 861 
10.04 836 

9.87 277 
9.87 266 
9.87 255 
9.87 243 
9.87 232 

15 

14 

13 

12 

11 

50 

51 

52 

53 

54 

9.82 410 
9.82 424 
9.82 439 
9.82 453 
9.82 467 

9.95 190 
9.95 215 
9.95 240 
9.95 266 
9.95 291 

10.04 810 
10.04 785 
10.04 760 
10.04 734 
10.04 709 

9.87 221 
9.87 209 
9.87 198 
9.87 187 
9.87 175 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.82 481 
9.82 495 
9.82 509 
9.82 523 
9.82 537 

9.95 317 
9.95 342 
9.95 368 
9.95 393 
9.95 418 

10.04 683 
10.04 658 
10.04 632 
10.04 607 
10.04 582 

9.87 164 
9.87 153 
9.87 141 
9.87 130 
9.87 119 

5 

4 

3 

2 

1 

60 

9.82 551 

9.95 444 

10.04 556 

9.87 107 

0 


L Cos 

d 

L Cot 1 c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


48 ' 




















































































VI 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


69 


42° 


' 

L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

9.82 551 


9.95 444 


10.04 556 

9.87 107 


60 




1 

9.82 565 

14 

9.95 469 

25 

10.04 531 

9.87 096 

11 

59 




2 

9.82 579 

14 

9.95 495 

26 

10.04 505 

9.87 085 

11 

58 




3 

9.82 593 

14 

9.95 520 

25 

10.04 480 

9.87 073 

12 

57 




4 

9.82 607 

14 

14 

9.95 545 

25 

26 

10.04 455 

9.87 062 

11 

12 

56 




5 

9.82 621 

9.95 571 

10.04 429 

9.87 050 

55 




6 

9.82 635 

14 

9.95 596 

25 

10.04 404 

9.87 039 

11 

54 




7 

9.82 649 

14 

9.95 622 

26 

10.04 378 

9.87 028 

11 

53 

„ 

26 

25 

8 

9.82 663 

14 

9.95 647 

25 

10.04 353 

9.87 016 

12 

52 


, 9 

9.82 677 

14 

14 

9.95 672 

25 

26 

10.04 328 

9.87 005 

11 

1 o 

51 

6 

2.6 

2.5 

10 

9.82 691 

9.95 698 

10.04 302 

9.86 993 

iz 

50 

7 

c 


2.9 

11 

9.82 705 

14 

9.95 723 

25 

10.04 277 

9.86 982 

11 

49 

9 


3 1 

12 

9.82 719 

14 

9.95 748 

25 

10.04 252 

9.86 970 

12 

48 

10 


4 2 

13 

9.82 733 

14 

9.95 774 

26 

10.04 226 

9.86 959 

11 

47 

20 


8.3 

14 

9.82 747 

14 

14 

9.95 799 

25 

26 

10 04 201 

9.86 947 

12 

11 

46 

30 

40 

\n 

lU 

15 

9.82 761 

9.95 825 

10.04 175 

9.86 936 

45 

50 

21.7 

208 

16 

9.82 775 

14 

9.95 850 

25 

10.04 150 

9.86 924 

12 

44 




17 

9.82 788 

13 

9.95 875 

25 

10.04 125 

9.86 913 

11 

43 




18 

9.82 802 

14 

9.95 901 

26 

10.04 099 

9.86 902 

11 

42 




19 

9.82 816 

14 

14 

9.95 926 

25 

26 

10.04 074 

9.86 890 

12 

11 

41 




20 

9.82 830 

9.95 952 

10.04 048 

9.86 879 

40 




21 

9.82 844 

14 

9.95 977 

25 

10.04 023 

9.86 867 

12 

39 




22 

9.82 858 

14 

9.96 002 

25 

10.03 998 

9.86 855 

12 

38 




23 

9.82 872 

14 

9.96 028 

26 

10.03 972 

9.86 844 

11 

37 




24 

9.82 885 

13 

14 

9.96 053 

25 

25 

10.03 947 

9.86 832 

12 

11 

36 




25 

9.82 899 

9.96 078 

10.03 922 

9.86 821 

35 




26 

9.82 913 

14 

9.96 104 

26 

10.03 896 

9.86 809 

12 

34 

ff 

14 

13 

27 

9.82 927 

14 

9.96 129 

25 

10.03 871 

9.86 798 

11 

33 




28 

9.82 941 

14 

9.96 155 

26 

10.03 845 

9.86 786 

12 

32 

6 

H 

1.3 

29 

9.82 955 

14 

1 Q 

9.96 180 

25 
o r; 

10.03 820 

9.86 775 

11 

12 

31 

7 

8 

1-9 

1.7 

30 

9.82 968 

io . 

9.96 205 


10.03 795 

9.86 763 

30 

9 

2.1 

2.0 

31 

9.82 982 

14 

9.96 231 

26 

10.03 769 

9.86 752 

11 

29 

10 



32 

9.82 996 

14 

9.96 256 

25 

10.03 744 

9.86 740 

12 

28 

20 

4.7 

4.3 

33 

9.83 010 

14 

9.96 281 

25 

10.03 719 

9.86 728 

12 

27 

30 

40 

93 

if 

34 

9.83 023 

13 

9.96 307 

26 
o ^ 

10.03 693 

9.86 717 

11 

12 

26 

50 

11.7 

10.8 

35 

9.83 037 

14 

9.96 332 


10.03 668 

9.86 705 i 

25 




36 

9.83 051 

14 

9.96 357 

25 

10.03 643 

9.86 694 

11 

24 




37 

9.83 065 

14 

9.96 383 

26 

10.03 617 

9.86 682 

12 

23 




38 

9.83 078 

13 

9.96 408 

25 

10.03 592 

9.86 670 

12 

22 




39 

9.83 092 

14 

9.96 433 

25 

9 A 

10.03 567 

9.86 659 

11 

12 

21 




40 

9.83 106 

14 

9.96 459 


10.03 541 

9.86 647 

20 




41 

9.83 120 

14 

9.96 484 

25 

10.03 516 

9.86 635 

12 

19 




42 

9.83 133 

13 

9.96 510 

26 

10.03 490 

9.86 624 

11 

18 




43 

9.83 147 

14 

9.96 535 

25 

10.03 465 

9.86 612 

12 

17 




44 

9.83 161 

14 

1 Q 

9.96 560 

25 

9 A 

10.03 440 

9.86 600 

12 

11 

16 




45 

9.83 174 

lo 

9.96 586 

ZD 

10.03 414 

9.86 589 

15 

" 

12 

11 

46 

9.83 188 

14 

9.96 611 

25 

10.03 389 

9.86 577 

12 

14 




47 

9.83 202 

14 

9.96 636 

25 

10.03 364 

9.86 565 

12 

13 

6 

7 

lA 

1.1 

48 

9.83 215 

13 

9.96 662 

26 

10.03 338 

9.86 554 

11 

12 

8 

1 6 

li 

49 

9.83 229 

14 

9.96 687 

25 

10.03 313 

9.86 542 

12 

12 

11 

9 

1.8 

1-6 

50 

9.83 242 

13 

9.96 712 

zo 

10.03 288 

9.86 530 

10 

10 

40 

37 

51 

9.83 256 

14 

9.96 738 

26 

10.03 262 

9.86 518 

12 

9 

zu 

30 

60 

5 5 

52 

9.83 270 

14 

9.96 763 

25 

10.03 237 

9.86 507 

11 

8 

40 

8.0 

7.3 

53 

9.83 283 

13 

9.96 788 

25 

10.03 212 

9.86 495 

12 

7 

50 

10.0 

9.2 

54 

9.83 297 

14 

9.96 814 

26 

9 A 

10.03 186 

9.86 483 

12 

11 

6 




55 

9.83 310 

13 

9.96 839 

zo 

10.03 161 

9.86 472 

5 




56 

9.83 324 

14 

9.96 864 

25 

10.03 136 

9.86 460 

12 

4 




57 

9.83 338 

14 

9.96 890 

. 26 

10.03 no 

9.86 448 

12 

3 




58 

9.83 351 

13 

9.96 915 

25 

10.03 085 

9.86 436 

12 

2 




59 

9.83 365 

14 

1 Q 

9.96 940 

25 

9A 

10.03 060 

9.86 425 

11 

12 

1 




60 

9.83 378 

lo 

9.96 966 


10.03 034 

9.86 413 

0 





L Cos 

d 

L Cot 

c d 

L Tan 

L Sin 

d 

' 

Prop. Pts. 


47 ' 







































































70 


FIVE-PLACE LOGARITHMS OF FUNCTIONS 


VI 


43 ° 



L Sin 

d 

L Tan 

c d 

L Cot 

L Cos 

d 


Prop. Pts. 

0 

9.83 378 


9.96 966 


10.03 034 

9.86 413 


60 




1 

9.83 392 

14 

9.96 991 

25 

10.03 009 

9.86 401 

12 

59 




2 

9.83 405 

13 

9.97 016 

25 

10.02 984 

9.86 389 

12 

58 




3 

9.83 419 

14 

9.97 042 

26 

10.02 9.58 

9.86 377 

12 

57 




4 

9.83 432 

13 

14 

9.97 067 

25 

25 

10.02 933 

9.86 366 

11 

1 9 

56 




5 

9.83 446 

9.97 092 

10.02 908 

9.86 354 


55 




6 

9.83 459 

13 

9.97 118 

26 

10.02 882 

9.86 342 

12 

54 




7 

9.83 473 

14 

9.97 143 

25 

10.02 857 

9.86 330 

12 

53 

„ 

26 

25 

8 

9.83 486 

13 

9.97 168 

25 

10.02 832 

9.86 318 

12 

52 




9 

9.83 500 

14 

9.97 193 

25 

10.02 807 

9.86 306 

12 

51 

6 

2.6 

2.5 











3.0 
3 5 

2.9 

3 3 

10 

9.83 513 


9.97 219 


10.02 781 

9.86 295 


50 

7 

11 

9.83 527 

14 

9.97 244 

25 

10.02 756 

9.86 283 

12 

49 

9 

3.9 

3^8 

12 

9.83 540 

13 

9.97 269 

25 

10.02 731 

9.86 271 

12 

48 

10 

4.3 

4.2 

13 

9.83 554 

14 

9.97 295 

26 

10.02 705 

9.86 259 

12 

47 

20 

8.7 

8.3 

14 

9.83 567 

13 

14 

9.97 320 

25 

10.02 680 

9.86 247 

12 

12 

46 

30 

40 

13.0 
17 3 

12.5 

16 7 

15 

9.83 581 


9.97 345 


10.02 655 

9.86 235 

45 

50 

21.7 

20.8 

16 

9.83 594 

13 

9.97 371 

26 

10.02 629 

9.86 223 

12 

44 




17 

9.83 608 

14 

9.97 396 

25 

10.02 604 

9.86 211 

12 

43 




18 

9.83 621 

13 

9.97 421 

25 

10.02 579 

9.86 200 

11 

42 




19 

9.83 634 

13 

14 

9.97 447 

26 

25 

10.02 553 

9.86 188 

12 

12 

41 




20 

9.83 648 

9.97 472 

10.02 528 

9.86 176 

40 




21 

9.83 661 

13 

9.97 497 

25 

10.02 503 

9.86 164 

12 

39 




22 

9.83 674 

13 

9.97 523 

26 

10.02 477 

9.86 152 

12 

38 




23 

9.83 688 

14 

9.97 548 

25 

10.02 452 

9.86 140 

12 

37 




24 

9.83 701 

13 

14 

9.97 573 

25 

25 

10.02 427 

9.86 128 

12 

12 

36 




25 

9.83 715 

9.97 598 

10.02 402 

9.86 116 

35 




26 

9.83 728 

13 

9.97 624 

26 

10.02 376 

9.86 104 

12 

34 

// 

14 

13 

27 

9.83 741 

13 

9.97 649 

25 

10.02 351 

9.86 092 

12 

33 




28 

9.83 755 

14 

9.97 674 

25 

10.02 326 

9.86 080 

12 

32 

6 

1.4 

1.3 

29 

9.83 768 

13 

13 

9.97 700 

26 

25 

10.02 300 

9.86 068 

12 

12 

31 

7 

8 

1.6 
1 9 

1.5 

1 7 

30 

9.83 781 

9.97 725 

10.02 275 

9.86 056 

30 

9 

2.1 

2.0 

31 

9.83 795 

14 

9.97 750 

25 

10.02 250 

9.86 044 

12 

29 

10 

2.3 

2.2 

32 

9.83 808 

13 

9.97 776 

26 

10.02 224 

9.86 032 

12 

28 

20 

4.7 

4.3 

33 

9.83 821 

13 

9.97 801 

25 

10.02 199 

9.86 020 

12 

27 

30 

40 

7.0 
9 3 

6.5 

8 7 

34 

9.83 834 

13 

14 

9.97 826 

25 

25 

10.02 174 

9.86 008 

12 

12 

26 

50 

ii;7 

io!8 

35 

9.83 848 

9.97 851 

10.02 149 

9.85 996 

25 




36 

9.83 861 

13 

9.97 877 

26 

10.02 123 

9.85 984 

12 

24 




37 

9.83 874 

13 

9.97 902 

25 

10.02 098 

9.85 972 

12 

23 




38 

9.83 887 

13 

9.97 927 

25 

10.02 073 

9.85 960 

12 

22 




39 

9.83 901 

14 

13 

9.97 953 

26 

O K 

10.02 047 

9.85 948 

12 

1 9 

21 




40 

9.83 914 

9.97 978 

ZD 

10.02 022 

9.85 936 

IZ 

20 




41 

9.83 927 

13 

9.98 003 

25 

10.01 997 

9.85 924 

12 

19 




42 

9.83 940 

13 

9.98 029 

26 

10.01 971 

9.85 912 

12 

18 




43 

9.83 954 

14 

9.98 054 

25 

10.01 946 

9.85 900 

12 

17 




44 

9.83 967 

13 

13 

9.98 079 

25 

25 

10.01 921 

9.85 888 

12 

12 

16 




45 

9.83 980 

9.98 104 

10.01 896 

9.85 876 

15 


12 

11 

46 

9.83 993 

13 

9.98 1.30 

26 

10.01 870 

9.85 864 

12 

14 




47 

9.84 006 

13 

9.98 155 

25 

10.01 845 

9.85 851 

13 

13 

6 

1.2 

1.1 

48 

9.84 020 

14 

9.98 180 

25 

10.01 820 

9.85 839 

12 

12 

7 

g 

1.4 

1.3 

49 

9.84 033 

13 

13 

9.98 206 

26 

25 

10.01 794 

9.85 827 

12 

12 

11 

9 

l.U 

1.8 

1.0 

1.6 

60 

9.84 046 

9.98 231 

10.01 769 

9.85 815 

10 

10 

2.0 

1.8 

51 

9.84 059 

13 

9.98 256 

25 

10.01 744 

9.85 803 

12 

9 

20 

4.0 

ft n 

3.7 

52 

9.84 072 

13 

9.98 281 

25 

10.01 719 

9.85 791 

12 

8 

ou 

40 

D.U 

8.0 

7^3 

53 

9.84 085 

13 

9.98 307 

26 

10.01 693 

9.85 779 

12 

7 

50 

10.0 

9.2 

54 

9.84 098 

13 

14 

9.98 332 

25 

25 

10.01 668 

9.85 766 

13 

12 

6 




55 

9.84 112 

9.98 357 

10.01 643 

9.85 754 

5 




56 

9.84 125 

13 

9.98 383 

26 

10.01 617 

9.85 742 

12 

4 




57 

9.84 138 

13 

9.98 408 

25 

10.01 592 

9.85 730 

12 

3 




58 

9.84 151 

13 

9.98 433 

25 

10.01 567 

9.85 718 

12 

2 




59 

9.84 164 

13 

13 

9.98 458 

25 

26 

10.01 542 

9.85 706 

12 

1 




60 

9.84 177 

9.98 484 

10.01 516 

9.85 693 

J.O 

0 





L Cos 

d 

L Cot 

Cd ! 

L Tan 

L Sin 

d 


Prop. Pts. 


46 ' 











































































Vi five-place logarithms of functions 71 


44° 


/ 

L Sin 

d 

L Tan 

cd 

LCot 

LCos 

d 


Prop. Pts. 

0 

1 

2 

3 

4 

9.84 177 
9.84 190 
9.84 203 
9.84 216 
9.84 229 

13 

13 

13 

13 

13 

13 

14 
13 
13 
13 

13 

13 

13 

13 

13 

12 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

13 

12 

13 

13 

13 

13 

13 

13 

12 

13 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

13 

12 

13 

13 

12 

13 

13 

12 

13 

13 

9.98 484 

9.98 509 
9.98 534 
9.98 560 
9.98 585 

25 

25 

26 
25 
25 

25 

26 
25 

25 

26 

25 

25 

25 

26 
25 

25 

25 

26 
25 

25 

26 
25 
25 

25 

26 

25 

25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
25 
25 

25 

26 

25 

25 

25 

26 
25 

25 

26 
25 
25 

25 

26 
*25 

25 

25 

26 
25. 
25 

25 

26 
25 

10.01 516 

10.01 491 
10.01 466 
10.01 440 
10.01 415 

9.85 693 
9.85 681 
9.85 669 
9.85 657 
9.85 645 

12 

12 

12 

12 

13 

12 

12 

12 

13 

12 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

12 

13 

12 

13 

12 

12 

13 

12 

13 

12 

13 

12 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

12 

13 

13 

12 

13 

12 

13 

12 

13 

13 

12 

13 

12 

60 

59 

58 

57 

56 

" 26 25 14 

6 2.6 2.5 1.4 

7 3.0 2.9 1.6 

8 3.5 3.3 1.9 

9 3.9 3.8 2.1 

10 4.3 4.2 2.3 

20 8.7 8.3 4.7 

30 13.0 12.5 7.0 

40 17.3 16.7 9.3 

50 21.7 20.8 11.7 

" 13 12 

6 1.3 1.2 

7 1.5 1.4 

8 1.7 1.6 

9 2.0 1.8 

10 2.2 2.0 

20 4.3 4.0 

30 6.5 6.0 

40 8.7 8.0 

50 10.8 10.0 

5 

6 

7 

8 

9 

9.84 242 
9.84 255 
9.84 269 
9.84 282 
9.84 295 

9.98 610 
9.98 635 
9.98 661 
9.98 686 
9.98 711 

10.01 390 
10.01 365 
10.01 339 
10.01 314 
10.01 289 

9.85 632 
9.85 620 
9.85 608 
9.85 596 
9.85 583 

55 

54 

53 

52 

51 

10 

11 

12 

13 

14 

9.84 308 
9.84 321 
9.84 334 
9.84 347 
9.84 360 

9.98 737 
9.98 762 
9.98 787 
9.98 812 
9.98 838 

10.01 263 
10.01 238 
10.01213 
10.01 188 
10.01 162 

9.85 571 
9.85 559 
9.85 547 
9.85 534 
9.85 522 

50 

49 

48 

47 

46 

15 

16 

17 

18 
19 

9.84 373 
9.84 385 
9.84 398 
9.84 411 
9.84 424 

9.98 863 
9.98 888 
9.98 913 
9.98 939 
9.98 964 

10.01 137 
10.01 112 
10.01 087 
10.01 061 
10.01 036 

9.85 510 
9.85 497 
9.85 485 
9.85 473 
9.85 460 

45 

44 

43 

42 

41 

20 

21 

22 

23 

24 

9.84 437 
9.84 450 
9.84 463 
9.84 476 
9.84 489 

9.98 989 

9.99 015 
9.99 040 
9.99 065 
9.99 090 

10.01 011 
10.00 985 
10.00 960 
10.00 935 
10.00 910 

9.85 448 
9.85 436 
9.85 423 
9.85 411 
9.85 399 

40 

39 

38 

37 

36 

25 

26 

27 

28 
29 

9.84 502 
9.84 515 
9.84 528 
9.84 540 
9.84 553 

9.99 116 
9.99 141 
9.99 166 
9.99 191 
9.99 217 

10.00 884 
10.00 859 
10.00 834 
10.00 809 
10.00 783 

9.85 386 
9.85 374 
9.85 361 
9.85 349 
9.85 337 

35 

34 

33 

32 

31 

30 

31 

32 

33 

34 

9.84 566 
9.84 579 
9.84 592 
9.84 605 
9.84 618 

9.99 242 
9.99 267 
9.99 293 
9.99 318 
9.99 343 

10.00 758 
10.00 733 
10.00 707 
10.00 682 
10.00 657 

9.85 324 
9.85 312 
9.85 299 
9.85 287 
9.85 274 

30 

29 

28 

27 

26 

35 

36 

37 

38 

39 

9.84 630 
9.84 643 
9.84 656 
9.84 669 
9.84 682 

9.99 368 
9.99 394 
9.99 419 
9.99 444 
9.99 469 

10.00 632 
10.00 606 
10.00 581 
10.00 556 
10.00 531 

9.85 262 
9.85 250 
9.^5 237 
9.85 225 
9.85 212 

25 

24 

23 

22 

21 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

9.84 694 
9.84 707 
9.84 720 
9.84 733 
9.84 745 

9.99 495 
9.99 520 
9.99 545 
9.99 570 
9.99 596 

10.00 505 
10.00 480 
10.00 455 
10.00 430 
10.00 404 

9.85 200 
9.85 187 
9.85 175 
9.85 162 
9.85 150 

20 

19 

18 

17 

16 

9.84 758 
9.84 771 
9.84 784 
9.84 796 
9.84 809 

9.99 621 
9.99 646 
9.99 672 
9.99 697 
9.99 722 

10.00 379 
10.00 354 
10.00 328 
10.00 303 
10.00 278 

9.85 137 
9.85 125 
9.85 112 
9.85 100 
9.85087 

15 

14 

13 

12 

11 

60 

51 

52 

53 

54 

9.84 822 
9.84 835 
9.84 847 
9.84 860 
9.84 873 

9.99 747 
9.99 773 
9.99 798 
9.99 823 
9.99 848 

10.00 253 
10.00 227 
10.00 202 
10.00 177 
10.00 152 

9.85 074 
9.85 062 
9.85 049 
9.85 037 
9.85 024 

10 

9 

8 

7 

6 

55 

56 

57 

58 

59 

9.84 885 
9.84 898 
9.84 911 
9.84 923 
9.84 936 

9.99 874 
9.99 899 
9.99 924 
9.99 949 
9.99 975 

10.00 126 
10.00 101 
10.00 076 
10.00 051 
10.00 025 

9.85 012 
9.84 999 
9.84 986 
9.84 974 
9.84 961 

5 

4 

3 

2 

1 

60 

9.84 949 

0.00 000 

10.00 000 

9.84 949 

0 


L Cos 

d 

L Cot 

c d [ L Tan 

L Sin 1 d 


Prop. Pts. 


45 ' 













































































TABLE VII 


COMMON LOGARITHMS 
OF NUMBERS 
FROM 

1 TO 10000 

TO 

FIVE DECIMAL PLACES 

1-100 


N 

Log 

N 

Log 

N 

Log 

N 

Log 

N 

Log 

0 

— 

20 

1. 30 103 

40 

1. 60 206 

CO 

1. 77 815 

80 

1. 90 309 

1 

0. 00 000 

21 

1. 32 222 

41 

1. 61 278 

61 

1. 78 533 

81 

1. 90 849 

2 

0. 30 103 

22 

1. 34 242 

42 

1. 62 325 

62 

1. 79 239 

82 

1. 91 381 

3 

0. 47 712 

23 

1. 36 173 

43 

1. 63 347 

63 

1. 79 934 

83 

1. 91 908 

4 

0. 60 206 

24 

1. 38 021 

44 

1, 64 345 

64 

1. 80 618 

84 

1. 92 428 

5 

0- 69 897 

25 

1. 39 794 

45 

1. 65 321 

65 

1. 81 291 

85 

1. 92 942 

6 

0. 77 815 

26 

1. 41 497 

46 

1. 66 276 

66 

1. 81 954 

86 

1. 93 450 

7 

0. 84 510 

27 

1. 43 136 

47 

1. 67 210 

67 

1. 82 607 

87 

1. 93 952 

8 

0. 90 309 

28 

1. 44 716 

48 

1. 68 124 

68 

1. 83 251 

88 

1. 94 448 

9 

0. 95 424 

29 

1, 46 240 

49 

1. 69 020 

69 

1. 83 885 

89 

1. 94 939 

10 

1. 00 000 

3D 

1. 47 712 

50 

1. 69 897 

70 

1. 84 510 

90 

1. 95 424 

n 

1. 04 139 

31 

1. 49 136 

51 

1. 70 757 

71 

1. 85 126 

91 

1. 95 904 

12 

1. 07 918 

32 

1. 50 515 

52 

1. 71 600 

72 

1. 85 733 

92 

1. 96 379 

13 

1. 11 394 

33 

1. 51 851 

53 

1. 72 428 

73 

1. 86 332 

93 

1. 96 848 

14 

1. 14 613 

34 

1. 53 148 

54 

1. 73 239 

74 

1. 86 923 

'94 

1. 97 313 

15 

1. 17 609 

35 

1. 54 407 

55 

1. 74 036 

75 

1. 87 506 

95 

1. 97 772 

16 

1. 20 412 

36 

1. 55 630 

56 

1. 74 819 

76 

1. 88 081 

96 

1. 98 227 

17 

1. 23 045 

37 

1. 56 820 

57 

1. 75 587 

77 

1. 88 649 

97 

1. 98 677 

18 

1. 25 527 

38 

1. 57 978 

58 

1. 76 343 

78 

1. 89 209 

98 

1. 99 123 

19 

1. 27 875 

39 

1. 59 106 

59 

1. 77 085 

79 

1. 89 763 

99 

1. 99 564 

20 

1. 30 103 

40 

1. 60 206 

60 

1. 77 815 

80 

1. 90 309 

100 

2. 00 000 


73 
























74 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


100-150 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

1 

8 

i_ 

i ^ 

Prop. Pts. 

100 

00 000 

043 

087 

130 

173 

217 

260 

303 

346 

389 





101 

432 

475 

518 

561 

604 

647 

689 

732 

.775 

817 





102 

860 

903 

945 

988 

*030 

*072 

*115 

*157 

*199 

*242 


44 

43 

42 

103 

01 284 

326 

368 

410 

452 

494 

536 

578 

620 

662 



104 

703 

745 

787 

828 

870 

912 

953 

995 

*036 

*078 

1 

4.4 

4.3 

4.2 









2 

8.8 

8.6 

8.4 

105 

02 119 

160 

202 

243 

284 

325 

366 

407 

449 

490 

3 

4 

13.2 
17 6 

12.9 
17 2 

12.6 

16.8 

21.0 

106 

531 

572 

612 

653 

694 

735 

776 

816 

857 

898 

5 

22^0 

2 i !5 

107 

938 

979 

*019 

*060 

*100 

*141 

*181 

*222 

*262 

*302 

6 

26.4 

25.8 

25.2 

108 

03 342 

383 

423 

463 

503 

543 

583 

623 

663 

703 

7 

30.8 

30.1 

29.4 

109 

743 

782 

822 

862 

902 

941 

981 

*021 

*060 

*100 

8 

9 

35.2 

39.6 

34.4 

38.7 

33.6 

37.8 

110 

04 139 

179 

218 

258 

297 

336 

376 

415 

454 

493 





111 

532 

571 

610 

650 

689 

727 

766 

805 

844 

883 


41 

40 

39 

112 

922 

961 

999 

*038 

*077 

*115 

*154. 

*192 

*231 

*269 


113 

05 308 

346 

385 

423 

461 

500 

538 

576 

614 

652 

1 

2 

4.1 

8.2 

4.0 

8.0 


114 

690 

729 

767 

805 

843 

881 

918 

956 

994 

*032 

3.9 

7.8 












3 

12.3 

12.0 

11.7 

115 

06 070 

108 

145 

183 

221 

258 

296 

333 

371 

408 

4 

16.4 

16.0 

15.6 

116 

446 

483 

521 

558 

595 

633 

670 

707 

744 

781 

5 

20.5 

20.0 

19.5 

117 

819 

856 

893 

930 

967 

*004 

*041 

*078 

*115 

*151 

6 

24.6 

24.0 

23.4 

118 

07 188 

225 

262 

298 

335 

372 

408 

445 

482 

518 

7 

8 

9 

28.7 

.32.8 

36.9 

28.0 

32.0 

36.0 

27.3 

31.2 

35.1 

119 

555 

591 

628 

664 

700 

737 

773 

809 

846 

882 

120 

918 

954 

990 

*027 

*063 

*099 

*135 

*171 

*207 

*243 





121 

08 279 

314 

350 

386 

422 

458 

493 

529 

565 

600 



37 


122 

636 

672 

707 

743 

778 

814 

849 

884 

920 

955 


OO 

OD 

123 

991 

*026 

*061 

*096 

*132 

*167 

*202 

*237 

*272 

*307 

1 

3.8 

3.7 

3.6 

124 

09 342 

377 

412 

447 

482 

517 

552 

587 

621 

656 

2 

7.6 

7.4 

7.2 












3 

11.4 

11.1 

10.8 

125 

691 

726 

760 

795 

830 

864 

899 

934 

968 

*003 

4 

15.2 

14.8 

14.4 

126 

10 037 

072 

106 

140 

175 

209 

243 

278 

312 

346 

5 

A 

19.0 

22.8 

26.6 

18.5 

22.2 

18.0 

21.6 

25.2 

127 

380 

415 

449 

483 

517 

551 

585 

619 

653 

687 

7 

25^9 

128 

721 

755 

789 

823 

857 

890 

924 

958 

992 

*025 

8 

30.4 

29.6 

28.8 

129 

11 059 

093 

126 

160 

193 

227 

261 

294 

327 

361 

9 

34.2 

33.3 

32.4 

130 

394 

428 

461 

494 

528 

561 

594 

628 

661 

694 





131 

727 

760 

793 

826 

860 

893 

926 

959 

992 

*024 


35 

34 

33 

132 

12 057 

090 

123 

156 

189 

222 

254 

287 

320 

352 



133 

385 

418 

450 

483 

516 

548 

581 

613 

646 

678 

1 

3.5 

3.4 

3.3 

134 

710 

743 

775 

808 

840 

872 

905 

937 

969 

*001 

2 

3 

7.0 

10.5 

6.8 

10.2 

6.6 

9.9 

135 

13 033 

066 

098 

130 

162 

194 

226 

258 

290 

322 

4 

5 

14.0 

17.5 

13.6 

17.0 

13.2 

16.5 

136 

354 

386 

418 

450 

481 

513 

545 

577 

609 

640 

6 

21.0 

20.4 

19.8 

137 

672 

704 

735 

767 

799 

830 

862 

893 

925 

956 

7 

24.5 

23.8 

23.1 

138 

988 

*019 

*051 

*082 

*114 

*145 

*176 

*208 

*239 

*270 

8 

28.0 

27.2 

26.4 

139 

14 301 

333 

364 

395 

426 

457 

489 

520 

551 

582 

9 

31.5 

30.6 

29.7 

140 

613 

644 

675 

706 

737 

768 

799 

829 

860 

891 




30 

141 

922 

953 

983 

*014 

*045 

*076 

*106 

*137 

*168 

*198 


32 

31 

142 

15 229 

259 

290 

320 

351 

381 

412 

442 

473 

503 

1 

2 

3.2 
6 4 

3.1 
6 2 

3.0 

6 0 

143 

534 

564 

594 

625 

655 

685 

715 

746 

776 

806 

144 

836 

866 

897 

927 

957 

987 

*017 

*047 

*077 

*107 

3 

9.6 

9:3 

9.0 












4 

12.8 

12.4 

12.0 

145 

16 137 

167 

197 

227 

256 

286 

316 

346 

376 

406 

5 

16.0 

15.5 

15.0 

146 

435 

465 

495 

524 

554 

584 

613 

643 

673 

702 

6 

19.2 

18.6 

18.0 

147 

732 

761 

791 

820 

850 

879 

909 

938 

967 

997 

7 

g 

22.4 
25 6 

21.7 
24 8 

21.0 

24 0 

148 

17 026 

056 

085 

114 

143 

173 

202 

231 

260 

289 

9 

28.8 

27^9 

27 !o 

149 

319 

348 

377 

406 

435 

464 

493 

522 

551 

580 


160 

609 

638 

667 

696 

725 

754 

782 

811 

840 

869 





N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 



























































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


75 


160-200 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 Prop. Pts. 

ISO 

17 609 

638 

667 

696 

725 

754 

782 

811 

840 

869 




151 

898 

926 

955 

984 

*013 

*041 

*070 

*099 

*127 

*156 




152 

18 184 

213 

241 

270 

298 

327 

355 

384 

412 

441 

29 

28 

153 

469 

498 

526 

554 

583 

611 

639 

667 

696 

724 



154 

752 

780 

808 

837 

865 

893 

921 

949 

977 

*005 1 

2.S 

1 2.8 











2 

5.8 

! 5.6 

155 

19 033 

061 

089 

117 

145 

173 

201 

229 

257 

285 4 

8.7 

8.4 

156 

312 

340 

368 

396 

424 

451 

479 

507 

535 

562 5 

11.6 

14.5 

1 11.2 
, 1 4. n 

157 

590 

618 

645 

673 

700 

728 

756 

783 

811 

838 6 

17^4 

16.8 

158 

866 

893 

921 

948 

976 

*003 

*030 

*058 

*085 

*112 7 

20.3 

19.6 

159 

20 140 

167 

194 

222 

249 

276 

303 

330 

358 

.385 8 

23.2 

22.4 












2fi.1 

25.2 

160 

412 

439 

466 

493 

520 

548 

575 

602 

629 

656 




161 

683 

710 

737 

763 

790 

817 

844 

871 

898 

925 




162 

952 

978 

*005 

*032 

*059 

*085 

*112 

*139 

*165 

*192 

27 

26 

163 

21 219 

245 

. 272 

299 

325 

352 

378 

405 

431 

458 1 




164 

484 

511 

537 

564 

590 

617 

643 

669 

696 

722 ^ 

2.7 

5.4 

2.6 

5.2 

165 

748 

775 

801 

827 

854 

880 

906 

932 

958 

3 

985 4 

8.1 

10.8 

7.8 

10.4 

166 

22 011 

037 

063 

089 

115 

141 

167 

194 

220 

246 5 

13.5 

13.0 

167 

272 

298 

324 

350 

376 

401 

427 

453 

479 

505 6 

16.2 

15.6 

168 

531 

557 

583 

608 

634 

660 

686 

712 

737 

763 1 

18.9 

oi A 

18.2 

169 

789 

814 

840 

866 

891 

917 

943 

968 

994 

*019 9 

.^1.0 

24.3 

20.8 

23.4 

170 

23 045 

070 

096 

121 

147 

172 

198 

223 

249 

274 




171 

300 

325 

350 

376 

401 

426 

452 

477 

502 

528 


OR 

172 

553 

578 

603 

629 

654 

679 

704 

729 

754 

779 



173 

805 

830 

855 

880 

905 

930 

955 

980 

*005 

*030 

1 

2.5 

174 

24 055 

080 

105 

130 

155 

180 

204 

229 

254 

279 

2 

5.0 











3 

7.5 

175 

304 

329 

353 

378 

403 

428 

452 

477 

502 

527 

4: 

10.0, 

176 

551 

576 

601 

625 

650 

674 

699 

724 

748 

773 ; 

5 

5 

12.5 

15 0 

177 

797 

822 

846 

871 

895 

920 

944 

969 

993 

*018 

7 

17!5 

178 

25 042 

066 

091 

115 

139 

164 

188 

212 

237 

261 8 

20.0 

179 

285 

310 

334 

358 

382 

406 

431 

455 

479 

503 < 

3 

22.5 

180 

527 

551 

1 575 

600 

624 

648 

672 

696 

720 

744 




181 

768 

792 

816 

840 

864 

888 

912 

935 

959 

983 

24 

23 

182 

26 007 

031 

055 

079 

102 

126 

150 

174 

198 

221 




183 

245 

269 

293 

316 

340 

364 

387 

411 

435 

458 1 

2.4 

2.3 

184 

482 

505 

529 

553 

576 

600 

623 

647 

670 

694 1 

4.8 

7.2 

4.6 

6.9 

185 

717 

741 

764 

788 

811 

834 

858 

881 

905 

928 5 

9.6 

12.0 

9.2 

11.5 

186 

951 

975 

998 

*021 

*045 

*068 

*091 

*114 

*138 

*161 6 

14.4 

13.8 

187 

27 184 

207 

231 

254 

277 

300 

323 

346 

370 

393 1 

16.8 

16.1 

188 

416 

439 

462 

485 

508 

531 

554 

577 

600 

623 g 

19.2 

18.4 

on 7 

189 

646 

669 

692 

715 

738 

761 

784 

807 

830 

852 ^ 



190 

875 

898 

921 

944 

967 

989 

*012 

*035 

*058 

*081 




191 

28 103 

126 

149 

171 

194 

217 

240 

262 

285 

307 

2i 

! 

21 

192 

330 

353 

375 

398 

421 

443 

466 

488 

511 

533 1 

2 2 

2 1 

193 

556 

578 

601 

623 

646 

668 

691 

713 

735 

758 2 

4A 

4.2 

194 

780 

803 

825 

847 

870 

892 

914 

937 

959 

981 3 

6 

.6 

6.3 











4 

8.8 

8.4 

195 

29 003 

026 

048 

070 

092 

115 

137 

159 

181 

203 ^ 

11.0 

1 Q O 

10.5 

1 O A 

196 

226 

248 

270 

292 

314 

336 

358 

380 

403 

425 2 

lo.2 

15 4 

14 7 

197 

447 

469 

491 

513 

535 

557 

579 

601 

623 

645 8 

17!6 

16!8 

198 

667 

688 

710 

732 

754 

776 

798 

820 

842 

863 9 

19.8 

18.9 

199 

885 

907 

929 

951 

973 

994 

*016 

*038 

*060 

*081 




200 

30 103 

125 

146 

168 

190 

211 

233 

255 

276 

298 




N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 Prop. Pts. 









































































76 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


200-250 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

200 

30 103 

125 

146 

168 

190 

211 

233 

255 I 

276 

298 





201 

320 

341 

363 

384 

406 

428 

449 

471 

492 

514 





202 

535 

557 

578 

600 

621 

643 

664 

685 1 

707 

728 


22 

21 

203 

750 

771 

792 

814 

835 

856 

878 

899 

920 

942 





204 

963 

984 

*006 

*027 

*048 

*069 

*091 

*112 

*133 

*154 

1 

2.2 

2.1 












2 - 

4.4 

4.2 

205 

31 175 

197 

218 

239 

260 

281 

302 

323 

345 

366 

3 

4 

6.6 
8 8 

6.3 

8 4 

206 

387 

408 

429 

450 

471 

492 

513 

534 

555 

576 

5 

11.0 

10.5 

207 

597 

618 

639 

660 

681 

702 

723 

744 

765 

785 

6 

13.2 

12.6 

208 

806 

827 

848 

869 

890 

911 

931 

952 

973 

994 

7 

15.4 

14.7 

209 

32 015 

035 

056 . 

077 

098 

118 

139 

160 1 

181 

201 

8 

9 

17.6 

19.8 

16.8 

18.9 

210 

222 

243 

263 

284 

305 

325 

346 

366 

387 

408 





211 

428 

449 

469 

490 

510 

531 

552 

572 

593 

613 





212 

634 

654 

675 

695 

715 

736 

756 

777 

797 

818 



20 

213 

838 

858 

879 

899 

919 

940 

960 

980 

*001 

*021 


1 

9 n 

214 

33 041 

062 

082 

102 

122 

143 

163 

183 

203 

224 


1 

2 

4.0 













3 

6.0 

215 

244 

264 

284 

304 

325 

345 

365 

385 

405 

425 


4 

8.0 

216 

445 

465 

486 

506 

526 

546 

566 

586 

606 

626 


5 

10.0 

217 

646 

666 

686 

706 

726 

746 

766 

786 

806 

826 


6 

12.0 

218 

846 

866 

885 

905 

925 

945 

965 

985 

*005 

*025 


t 

g 

16 0 

219 

34 044 

064 

084 

104 

124 

143 

163 

183 

203 

223 


9 

18.0 

220 

242 

262 

282 

301 

321 

341 

361 

380 

400 

420 





221 

439 

459 

479 

498 

518 

537 

557 

577 

596 

616 



ia 

222 

635 

655 

674 

694 

713 

733 

753 

772 

792 

811 





223 

830 

850 

869 

889 

908 

928 

947 

967 

986 

*005 


1 

1.9 

224 

35 025 

044 

064 

083 

102 

122 

141 

160 

180 

199 


2 

3.8 













3 

5.7 

225 

218 

238 

257 

276 

295 

315 

334 

353 

372 

392 


4 

c 

7.6 

Q ’i 

226 

411 

430 

449 

468 

488 

507 

526 

545 

564 

583 


6 

v.o 

11.4 

227 

603 

622 

641 

660 

679 

698 

717 

736 

755 

774 


7 

13.3 

228 

793 

813 

832 

851 

870 

889 

908 

927 

946 

965 

8 

15.2 

229 

984 

*003 

*021 

*040 

*059 

*078 

*097 

*116 

*135 

*154 


9 

17.1 

230 

36 173 

192 

211 

229 

248 

267 

286 

305 

324 

342 





231 

361 

380 

399 

418 

436 

455 

474 

493 

511 

530 



18 

232 

549 

568 

586 

605 

624 

642 

661 

680 

698 

717 





233 

736 

754 

773 

791 

810 

829 

847 

866 

884 

903 


1 

1.8 

234 

922 

940 

959 

977 

996 

*014 

*033 

*051 

*070 

*088 


2 

3 

3.6 

5.4 













4 

7.2 

235 

37 107 

125 

144 

162 

181 

199 

218 

236 

254 

273 


5 

9.0 

236 

291 

310 

328 

346 

365 

383 

401 

420 

438 

457 


6 

10.8 

237 

475 

493 

511 

530 

548 

566 

585 

603 

621 

639 


7 

12.6 

238 

658 

676 

694 

712 

731 

749 

767 

785 

803 

822 

o 

n 

14.4 

1 A 9 

239 

840 

858 

876 

894 

912 

931 

949 

967 

985 

*003 





240 

38 021 

039 

057 

075 

093 

112 

130 

148 

! 166 

184 





241 

202 

220 

238 

256 

274 

292 

310 

328 

1 346 

364 



17 

242 

382 

399 

417 

435 

453 

471 

489 

507 

525 

543 


1 

1 7 

243 

561 

578 

596 

614 

632 

650 

668 

686 

703 

721 


2 

3.4 

244 

739 

757 

775 

792 

810 

828 

846 

863 

881 

899 


3 

S 














4 

6.8 

245 

917 

934 

952 

970 

987 

*005 

*023 

*041 

*058 

*076 

5 

ft 

8.5 

246 

39 094 

111 

129 

146 

164 

182 

199 

217 

235 

252 

D 

7 

lU.Z 

11 9 

247 

270 

287 

305 

322 

340 

358 

375 

393 

410 

428 

8 

13.6 

248 

445 

463 

480 

498 

515 

533 

550 

568 

585 

602 


9 

15.3 

249 

620 

637 

655 

672 

690 

707 

724 

742 

759 

777 





250 

794 

811 

829 

846 

863 

881 

898 

915 

933 

950 





N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 



















































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 

260-300 


77 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

250 

39 794 

811 

829 

846 

863 

881 

898 

915 

933 

950 



251 

967 

985 

*002 

*019 

*037 

*054 

*071 

*088 

*106 

*123 



252 

40 140 

157 

175 

192 

209 

226 

243 

261 

278 

295 


18 

253 

312 

329 

346 

364 

381 

398 

415 

432 

449 

466 


254 

483 

500 

518 

535 

552 

569 

586 

603 

620 

637 

1 

1.8 

255 










2 

3.6 

654 

671 

688 

705 

722 

739 

756 

773 

790 

807 

3 

5.4 

256 

824 

841 

858 

875 

892 

909 

926 

943 

960 

976 

4 

7.2 

257 

993 

*010 

*027 

*044 

*061 

*078 

*095 

*111 

*128 

*145 

5 

6 

9.0 

10 8 


41 162 

179 

196 

212 

229 

246 

263 

280 

296 

313 

7 

12;6 

259 

330 

347 

363 

380 

397 

414 

430 

447 

464 

481 

8 

9 

14.4 

16.2 

260 

497 

514 

531 

547 

564 

581 

597 

614 

631 

647 


261 

664 

681 

697 

714 

731 

747 

764 

780 

797 

814 



262 

830 

847 

863 

880 

896 

913 

929 

946 

963 

979 


17 

263 

996 

*012 

*029 

*045 

*062 

*078 

*095 

*111 

*127 

*144 


1.7 

3.4 

264 

42 160 

177 

193 

210 

226 

243 

259 

275 

292 

308 

1 

2 

265 

325 

341 

357 

374 

390 

406 

423 

439 

455 

472 

3 

4 

5.1 

6.8 

266 

488 

504 

521 

537 

553 

570 

586 

602 

619 

635 

5 

8.5 

267 

651 

667 

684 

700 

716 

732 

749 

765 

781 

797 

6 

10.2 

268 

813 

830 

846 

862 

878 

894 

911 

927 

943 

959 

7 

11.9 

269 

975 

991 

*008 

*024 

*040 

*056 

*072 

*088 

*104 

*120 

8 

9 

13.6 

15.3 

270 

43 136 

152 

169 

185 

201 

217 

233 

249 

265 

281 



271 

297 

313 

329 

345 

361 

377 

393 

409 

425 

441 


16 

272 

457 

473 

489 

505 

521 

537 

553 

569 

584 

600 


273 

616 

632 

648 

664 

680 

696 

712 

727 

743 

759 

1 

1 6 

274 

775 

791 

807 

823 

838 

854 

870 

886 

902 

917 

2 

i.2 











3 

4.8 

275 

933 

949 

965 

981 

996 

*012 

*028 

*044 

*059 

*075 

4 

6.4 

276 

44 091 

107 

122 

138 

154 

170 

185 

201 

217 

232 

5 

8.0 

277 

248 

264 

279 

295 

311 

326 

342 

358 

373 

389 

7 

112 

278 

404 

420 

436 

451 

467 

483 

498 

514 

529 

545 

8 

12.8 

279 

560 

576 

592 

607 

623 

638 

654 

669 

685 

700 

9 

14.4 

280 

716 

731 

747 

762 

778 

793 

809 

824 

840 

855 



281 

871 

886 

902 

917 

932 

948 

963 

979 

994 

*010 


16 

282 

45 025 

040 

056 

071 

086 

102 

117 

133 

148 

163 


283 

179 

194 

209 

225 

240 

255 

271 

286 

301 

317 

1 

1.5 

284 

332 

347 

362 

378 

393 

408 

423 

439 

454 

469 

2 

3 

3.0 

4.5 

285 

484 

500 

515 

530 

545 

561 

576 

591 

606 

621 

4 

5 

6.0 

7.5 

286 

637 

652 

667 

682 

697 

712 

728 

743 

758 

773 

6 

9.0 

287 

788 

803 

818 

834 

849 

864 

879 

894 

909 

924 

7 

10.5 

288 

939 

954 

969 

984 

*000 

*015 

*030 

*045 

*060 

*075 

8 

12.0 

13.5 

289 

46 090 

105 

120 

135 

150 

165 

180 

195 

210 

225 

9 

290 

240 

255 

270 

285 

300 

315 

330 

345 

359 

374 


14 

291 

389 

404 

419 

434 

449 

464 

479 

494 

509 

523 


292 

538 

553 

568 

583 

598 

613 

627 

642 

657 

672 

\ 

1.4 

2.8 

293 

687 

702 

716 

731 

746 

761 

776 

790 

805 

820 

2 

294 

835 

850 

864 

879 

894 

909 

923 

938 

953 

967 

3 

4.2 












4 

5.6 

295 

982 

997 

*012 

*026 

*041 

*056 

*070 

*085 

*100 

*114 

5 

7.0 

8.4 

9 8 

296 

47 129 

144 

159 

173 

188 

202 

217 

232 

246 

261 

6 

7 

297 

276 

290 

305 

319 

334 

349 

363 

378 

392 

407 

8 

11 !2 

298 

422 

436 

451 

465 

480 

494 

509 

524 

538 

553 

9 

12.6 

299 

567 

582 

596 

611 

625 

640 

654 

669 

683 

698 



300 

712 

727 

741 

756 

770 

784 

799 

813 

828 

842 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 


log e = .43429 





























































78 FIVE-PLACE LOGARITHMS OF NUMBERS VII 


300-360 


N 

L 0 

1 

2 

3 

4 


6 

7 

8 

9 

Prop. Pts. 

300 

47 712 

727 

741 

756 

770 

784 

799 

813 

828 

842 



301 

857 

871 

885 

900 

914 

929 

943 

958 

972 

986 



302 

48 001 

015 

029 

044 

058 

073 

087 

101 

116 

130 



303 

144 

159 

173 

187 

202 

216 

230 

244 

259 

273 



304 

287 

302 

316 

330 

344 

359 

373 

387 

401 

416 


rl5 

305 

430 

444 

458 

473 

487 

501 

515 

530 

544 

558 

1 

1.5 

306 

572 

586 

601 

615 

629 

643 

657 

671 

686 

700 

2 

3.0 

307 

714 

728 

742 

756 

770 

785 

799 

813 

827 

841 

3 

4.5 

308 

855 

869 

883 

897 

911 

926 

940 

954 

968 

982 

4 

5 

6.0 

7 5 

309 

996 

*010 

*024 

*038 

*052 

*066 

*080 

*094 

*108 

*122 

6 

9!o 












7 

10 5 














310 

49 136 

150 

164 

178 

192 

206 

220 

234 

248 

262 

8 

12!o 

311 

276 

290 

304 

318 

332 

346 

360 

374 

388 

402 

9 

13.5 

312 

415 

429 

443 

457 

471 

485 

499 

513 

527 

541 



313 

554 

568 

582 

596 

610 

624 

638 

651 

665 

679 



314 

693 

707 

721 

734 

748 

762 

776 

790 

803 

817 



315 

831 

845 

859 

872 

886 

900 

914 

927 

941 

955 


1A 

316 

969 

982 

996 

*010 

*024 

*037 

*051 

*065 

*079 

*092 



317 

50 106 

120 

133 

147 

161 

174 

188 

202 

215 

229 

1 

1.4 

318 

243 

256 

270 

284 

297 

311 

325 

338 

352 

365 

2 

2.8 

319 

379 

393 

406 

420 

433 

447 

461 

474 

488 

501 

3 

4.2 












4 

5.6 

320 

515 

529 

542 

556 

569 

583 

596 

610 

623 

637 

5 

6 

7.0 

8 4 

321 

651 

664 

678 

691 

705 

718 

732 

745 

759 

772 

7 

9.8 

322 

786 

799 

813 

826 

840 

853 

866 

880 

893 

907 

8 

11.2 

323 

920 

934 

947 

961 

974 

987 

*001 

*014 

*028 

*041 

9 

12.6 

324 

51 055 

068 

081 

095 

108 

121 

135 

148 

162 

175 



325 

188 

202 

215 

228 

242 

255 

268 

282 

295 

308 



326 

322 

335 

348 

362 

375 

388 

402 

415 

428 

441 



327 

455 

468 

481 

495 

508 

521 

534 

548 

561 

574 


13 

328 

587 

601 

614 

627 

640 

654 

667 

680 

693 

706 


329 

720 

733 

746 

759 

772 

786 

799 

812 

825 

838 

1 

o 

1.3 

O A 

330 

851 

865 

878 

891 

904 

917 

930 

943 

957 

970 

3 

Z.O 

3.9 

331 

983 

996 

*009 

*022 

*035 

*048 

*061 

*075 

*088 

*101 

4 

5.2 

332 

52 114 

127 

140 

153 

166 

179 

192 

205 

218 

231 

0 

7 8 

333 

244 

257 

270 

284 

297 

310 

323 

336 

349 

362 

7 

9^1 

334 

375 

388 

401 

414 

427 

440 

453 

466 

479 

492 

8 

10.4 












9 

11.7 

335 

504 

517 

530 

543 

556 

569 

582 

595 

608 

621 



336 

634 

647 

660 

673 

686 

699 

711 

724 

737 

750 



337 

763 

776 

789 

802 

815 

827 

840 

853 

866 

879 



338 

892 

905 

917 

930 

943 

956 

969 

982 

994 

*007 



339 

53 020 

033 

046 

058 

071 

084 

097 

110 

122 

135 


12 

340 

148 

161 

173 

186 

199 

212 

224 

237 

250 

263 


1 2 

341 

275 

288 

301 

314 

326 

339 

352 

364 

377 

390 

2 

2^4 

342 

403 

415 

428 

441 

453 

466 

479 

491 

504 

517 

3 

3.6 

343 

529 

542 

555 

567 

580 

593 

605 

618 

631 

643 

4 

4.8 

344 

656 

668 

681' 

694 

706 

719 

732 

744 

757 

769 

5 

6 

6.0 

7.2 

345 

782 

794 

807 

820 

832 

845 

857 

870 

882 

895 

7 

8 

8.4 

9.6 

346 

908 

920 

933 

945 

958 

970 

983 

995 

*008 

*020 

9 

10.8 

347 

54 033 

045 

058 

070 

083 

095 

108 

120 

133 

145 



348 

158 

170 

183 

195 

208 

220 

233 

245 

258 

270 



349 

283 

295 

307 

320 

332 

345 

357 

370 

382 

394 



350 

407 

419 

432 

444 

456 

469 

481 

494 

506 

518 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 


log TT = .49715 








































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


79 


360-400 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

350 

54 407 

419 

432 

444 

456 

469 

481 

494 

506 

518 



351 

531 

543 

555 

568 

580 

593 

605 

617 

630 

642 



352 

654 

667 

679 

691 

704 

716 

728 

741 

753 

765 



353 

777 

790 

802 

814 

827 

839 

851 

864 

876 

888 


13 

354 

900 

913 

925 

937 

949 

962 

974 

986 

998 

*011 


355 

55 023 

035 

047 

060 

072 

084 

096 

108 

121 

133 

1 

2 

1.3 

2.6 

356 

145 

157 

169 

182 

194 

206 

218 

230 

242 

255 

3 

3.9 

357 

267 

279 

291 

303 

315 

328 

340 

352 

364 

376 

4 

5.2 

358 

388 

400 

413 

425 

437 

449 

461 

473 

485 

497 

5 

6.5 

7.8 

9.1 

10.4 

11.7 

359 

509 

522 

534 

546 

558 

570 

582 

594 

606 

618 

7 

360 

630 

642 

654 

666 

678 

691 

703 

715 

727 

739 

8 

9 

361 

751 

763 

775 

787 

799 

811 

823 

835 

847 

859 



362 

871 

883 

895 

907 

919 

931 

943 

955 

967 

979 



363 

991 

*003 

*015 

*027 

*038 

*050 

*062 

*074 

*086 

*098 



364 

56 110 

122 

134 

146 

158 

170 

182 

194 

205 

217 



365 

229 

241 

253 

265 

277 

289 

301 

312 

324 

336 


12 

366 

348 

360 

372 

384 

396 

407 

419 

431 

443 

455 

1 

2 

1.2 

2.4 

3.6 

367 

467 

478 

490 

502 

514 

526 

538 

549 

561 

573 

368 

585 

597 

608 

620 

632 

644 

656 

667 

679 

691 

3 

369 

703 

714 

726 

738 

750 

761 

773 

785 

797 

808 

4 

4.8 











5 

6.0 

370 

820 

832 

844 

855 

867 

879 

891 

902 

914 

926 

6 

7 

7.2 

8 4 

371 

937 

949 

961 

972 

984 

996 

*008 

*019 

*031 

*043 

8 

9!6 

372 

57 054 

066 

078 

089 

101 

113 

124 

136 

148 

159 

9 

10.8 

373 

171 

183 

194 

206 

217 

229 

241 

252 

264 

276 



374 

287 

299 

310 

322 

334 

345 

357 

368 

380 

392 



375 

403 

415 

426 

438 

449 

461 

473 

484 

496 

507 



376 

519 

530 

542 

553 

565 

576 

588 

600 

611 

623 



377 

634 

646 

657 

669 

680 

692 

703 

715 

726 

738 


11 

378 

749 

761 

772 

784 

795 

807 

818 

830 

841 

852 


1.1 

2.2 

379 

864 

875 

887 

898 

910 

921 

933 

944 

955 

967 

1 

2 

380 

978 

990 

*001 

*013 

*024 

*035 

*047 

*058 

*070 

*081 

3 

4 

3.3 

4.4 

381 

58 092 

104 

115 

127 

138 

149 

161 

172 

184 

195 

5 

5.5 

382 

206 

218 

229 

240 

252 

263 

274 

286 

297 

309 

6 

6.6 - 

383 

320 

331 

343 

354 

365 

377 

388 

399 

410 

422 

7 

Q 

7.7 
s s 

384 

433 

444 

456 

467 

478 

490 

501 

512 

524 

535 

O 

9 

0.0 

9.9 

385 

546 

557 

569 

580 

591 

602 

614 

625 

636 

647 



386 

659 

670 

681 

692 

704 

715 

726 

737 

749 

760 



387 

771 

782 

794 

805 

816 

827 

838 

850 

861 

872 



388 

883 

894 

906 

917 

928 

939 

950 

961 

973 

984 



389 

995 

*006 

*017 

*028 

*040 

*051 

*062 

*073 

*084 

*095 


10 

390 

59 106 

118 

129 

140 

151 

162 

173 

184 

195 

207 

1 

1.0 

391 

218 

229 

240 

251 

262 

273 

284 

295 

306 

318 

2 

2.0 

3.0 

4 0 

392 

329 

340 

351 

362 

373 

384 

395 

406 

417 

428 

3 

4 

393 

439 

450 

461 

472 

483 

494 

506 

517 

528 

539 

5 

5!o 

394 

550 

561 

572 

583 

594 

605 

616 

627 

638 

649 

6 

6.0 











7 

7.0 

395 

660 

671 

682 

693 

704 

715 

726 

737 

748 

759 

8 

8.0 

9.0 

396 

770 

780 

791 

802 

813 

824 

835 

846 

857 

868 

9 

397 

879 

890 

901 

912 

923 

934 

945 

956 

966 

977 



398 

988 

999 

*010 

*021 

*032 

*043 

*054 

*065 

*076 

*086 



399 

60 097 

108 

119 

130 

141 

152 

163 

173 

184 

195 



400 

206 

217 

228 

239 

249 

260 

271 

282 

293 

304 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

































































80 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


400-450 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

400 

60 206 

217 

228 

239 

249 

260 

271 

282 

293 

304 



401 

314 

325 

336 

347 

358 

369 

379 

390 

401 

412 



402 

423 

433 

444 

455 

466 

477 

487 

498 

509 

520 



403 

531 

541 

552 

563 

574 

584 

595 

606 

617 

627 



404 

' 638 

649 

660 

670 

681 

692 

703 

713 

724 

735 



405 

746 

756 

767 

778 

788 

799 

810 

821 

831 

842 



406 

853 

863 

874 

885 

895 

906 

917 

927 

938 

949 


n 

407 

959 

970 

981 

991 

*002 

*013 

*023 

*034 

*045 

*055 



408 

61 066 

077 

087 

098 

109 

119 

130 

140 

151 

162 

1 

1.1 

409 

172 

183 

194 

204 

215 

225 

236 

247 

257 

268 

2 

3 

2.2 

3.3 

410 

278 

289 

300 

310 

321 

331 

342 

352 

363 

374 

4 

5 

4.4 

5.5 

411 

384 

395 

405 

416 

426 

437 

448 

458 

469 

479 

6 

6.6 

412 

490 

500 

511 

521 

532 

542 

553 

563 

574 

584 

7 

7.7 

413 

595 

606 

616 

627 

637 

648 

658 

669 

679 

690 

8 

Q 

8.8 

Q Q 

414 

700 

711 

721 

731 

742 

752 

763 

773 

784 

794 

y 

y .y 

415 

805 

815 

826 

836 

847 

857 

868 

878 

888 

899 



416 

909 

920 

930 

941 

951 

962 

972 

982 

993 

*003 



417 

62 014 

024 

034 

045 

055 

066 

076 

086 

097 

107 



418 

118 

128 

138 

149 

159 

170 

180 

190 

201 

211 



419 

221 

232 

242 

252 

263 

273 

284 

294 

304 

315 



420 

325 

335 

346 

356 

366 

377 

387 

397 

408 

418 



421 

428 

439 

449 

459 

469 

480 

490 

500 

511 

521 


10 

422 

531 

542 

552 

562 

572 

583 

593 

603 

613 

624 



423 

634 

644 

655 

665 

675 

685 

696 

706 

716 

726 

1 

1.0 

424 

737 

747 

757 

767 

778 

788 

798 

808 

818 

829 

2 

2.0 












3 

3.0 

425 

839 

849 

859 

870 

880 

890 

900 

910 

921 

931 

4 

4.0 

426 

941 

951 

961 

972 

982 

992 

*002 

*012 

*022 

*033 

O 

6 

o.u 

6.0 

427 

63 043 

053 

063 

073 

083 

094 

104 

114 

124 

134 

7 

7.0 

428 

144 

155 

165 

175 

185 

195 

205 

215 

225 

236 

8 

8.0 

429 

246 

256 

266 

276 

286 

296 

306 

317 

327 

337 

9 

9.0 

430 

347 

357 

367 

377 

387 

397 

407 

417 

428 

438 



431 

448 

458 

468 

478 

488 

498 

508 

518 

528 

538 



432. 

548 

558 

568 

579 

589 

599 

609 

619 

629 

639 



433 

649 

659 

669 

679 

689 

699 

709 

719 

729 

739 



434 

749 

759 

769 

779 

789 

799 

809 

819 

829 

839 



435 

849 

859 

869 

879 

889 

899 

909 

919 

929 

939 



436 

949 

959 

969 

979 

988 

998 

*008 

*018 

*028 

*038 



437 

64 048 

058 

068 

078 

088 

098 

108 

118 

128 

137 


9 

438 

147 

157 

167 

177 

187 

197 

207 

217 

227 

237 


0 9 

439 

246 

256 

266 

276 

286 

296 

306 

316 

326 

335 

2 

1.8 













O 7 














440 

345 

355 

365 

375 

385 

395 

404 

414 

424 

434 

4 

3.6 

441 

444 

454 

464 

473 

483 

493 

503 

513 

523 

532 

5 

A 

4.5 

442 

542 

552 

562 

572 

582 

591 

601 

611 

621 

631 

o 

7 

6.3 

443 

640 

650 

660 

670 

680 

689 

699 

709 

719 

729 

8 

7.2 

444 

738 

748 

758 

768 

777 

787 

797 

807 

816 

826 

9 

8.1 

445 

836 

846 

856 

865 

875 

885 

895 

904 

914 

924 



446 

933 

943 

953 

963 

972 

982 

992 

*002 

*011 

*021 



447 

65 031 

040 

050 

060 

070 

079 

089 

099 

108 

118 



448 

128 

137 

147 

157 

167 

176 

186 

196 

205 

215 



449 

225 

234 

244 

254 

263 

273 

283 

292 

302 

312 



450 

321 

331 

341 

350 

360 

369 

379 

389 

398 

408 



N 

L 0 

1 

2 

3 

4 

5 

i 

6 

7 

8 

9 

Prop. Pts. 













































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


81 


450-600 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

450 

65 321 

331 

341 

350 

360 

369 

379 

389 

398 

408 



451 

418 

427 

437 

447 

456 

466 

475 

485 

495 

504 



452 

514 

523 

533 

543 

552 

562 

571 

581 

591 

600 



453 

610 

619 

629 

639 

648 

658 

667 

677 

686 

696 



454 

706 

715 

725 

734 

744 

753 

763 

772 

782 

792 



455 

801 

811 

820 

830 

839 

849 

858 

868 

877 

887 



456 

896 

906 

916 

925 

935 

944 

954 

963 

973 

982 


10 

457 

992 

*001 

*011 *020 

*030 

*039 

*049 

*058 

*068 

*077 


458 

66 087 

096 

106 

115 

124 

134 

143 

153 

162 

172 

1 

1.0 

459 

181 

191 

200 

210 

219 

229 

238 

247 

257 

266 

2 

3 

2.0 

3.0 

460 

276 

285 

295 

304 

314 

323 

332 

342 

351 

361 

4 

5 

4.0 

5.0 

461 

370 

380 

389 

398 

408 

417 

427 

436 

445 

455 

6 

6.0 

462 

464 

474 

483 

492 

502 

511 

521 

530 

539 

549 

7 

7.0 

463 

558 

567 

577 

586 

596 

605 

614 

624 

633 

642 

8 

9 

8.0 

9.0' 

464 

652 

661 

671 

680 

689 

699 

708 

717 

727 

736 


465 

745 

755 

764 

773 

783 

792 

801 

811 

820 

829 



466 

839 

848 

857 

867 

876 

885 

894 

904 

913 

922 



467 

932 

941 

950 

960 

969 

978 

987 

997 

*006 

*015 



468 

67 025 

034 

043 

052 

062 

071 

080 

089 

099 

108 



469 

117 

127 

136 

145 ■ 

154 

164 

173 

182 

191 

201 



470 

210 

219 

228 

237 

247 

256 

265 

274 

284 

293 



471 

302 

311 

321 

330 

339 

348 

357 

367 

376 

385 


9 

472 

394 

403 

413 

422 

431 

440 

449 

459 

468 

477 



473 

486 

495 

504 

514 

523 

532 

541 

550 

560 

569 

1 

0.9 

474 

578 

587 

596 

605 

614 

624 

633 

642 

651 

660 

2 

3 

1.8 

2.7 

475 

669 

679 

688 

697 

706 

715 

724 

733 

742 

752 

4 

5 

3.6 

4 5 

476 

761 

770 

779 

788 

797 

806 

815 

825 

834 

843 

6 

5.4 

477 

852 

861 

870 

879 

888 

897 

906 

916 

925 

934 

7 

6.3 

478 

943 

952 

961 

970 

979 

988 

997 

*006 

*015 

*024 

8 

7.2 

479 

68 034 

043 

052 

061 

070 

079 

088 

097 

106 

115 

9 

8.1 

480 

124 

133 

142 

151 

160 

169 

178 

187 

196 

205 



481 

215 

224 

233 

242 

251 

260 

269 

278 

287 

296 



482 

305 

314 

323 

332 

341 

350 

359 

368 

377 

386 



483 

395 

404 

413 

422 

431 

440 

449 

458 

467 

476 



484 

485 

494 

502 

511 

520 

529 

538 

547 

556 

565 



485 

574 

583 

592 

601 

610 

619 

628 

637 

646 

655 



486 

664 

673 

681 

690 

699 

708 

717 

726 

735 

744 


o 

487 

753 

762 

771 

780 

789 

797 

806 

815 

824 

833 


o 

488 

842 

851 

860 

869 

878 

886 

895 

904 

913 

922 

1 

0.8 

489 

931 

940 

949 

958 

966 

975 

984 

993 

*002 

*011 

2 

1.6 











3 

2.4 

3.2 

4.0 

4.8 

490 

69 020 

028 

037 

046 

055 

064 

073 

082 

090 

099 

4 

r 

491 

108 

117 

126 

135 

144 

152 

161 

170 

179 

188 

O 

6 

492 

197 

205 

214 

223 

232 

241 

249 

258 

267 

276 

7 

5.6 

493 

285 

294 

302 

311 

320 

329 

338 

346 

355 

364 

8 

6.4 

494 

373 

381 

390 

399 

408 

417 

425 

434 

443 

452 

9 

7.2 

495 

461 

469 

478 

487 

496 

504 

513 

522 

531 

539 



496 

548 

557 

556 

574 

583 

592 

601 

609 

618 

627 



497 

636 

644 

653 

662 

671 

679 

688 

697 

705 

714 



498 

723 

732 

740 

749 

758 

767 

775 

784 

793 

801 



499 

810 

819 

827 

836 

845 

854 

862 

871 

880 

888 



500 

897 

906 

914 

i 923 

932 

940 

949 

958 

966 

975 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 































































82 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


600-550 



L 0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Prop. Pts. 

500 

69 897 

906 

914 

923 

932 

940 

949 

958 

966 

975 



501 

984 

992 

*001 

*010 

*018 

*027 

*036 

*044 

*053 

*062 



502 

70 070 

079 

088 

096 

105 

114 

122 

131 

140 

148 



503 

157 

165 

174 

183 

191 

200 

209 

217 

226 

234 



504 

243 

252 

260 

269 

278 

286 

295 

303 

312 

321 



505 

329 

338 

346 

355 

364 

372 

381 

389 

398 

406 



506 

415 

424 

432 

441 

449 

458 

467 

475 

484 

492 


9 

507 

501 

509 

518 

526 

535 

544 

552 

561 

569 

578 



508 

586 

595 

603 

612 

621 

629 

638 

646 

655 

663 

1 

0.9 

509 

672 

680 

689 

697 

706 

714 

723 

731 

740 

749 

2 

1.8 












3 

2.7 

510 

757 

766 

774 

783 

791 

800 

808 

817 

825 

834 

4 

5 

3.6 

4.5 

511 

842 

851 

859 

868 

876 

885 

893 

902 

910 

919 

6 

5.4 

512 

927 

935 

944 

952 

961 

969 

978 

986 

995 

*003 

7 

6.3 

513 

71 012 

020 

029 

037 

046 

054 

063 

071 

079 

088 

8 

7.2 

8.1 

514 

096 

105 

113 

122 

130 

139 

147 

155 

164 

172 

9 

515 

181 

189 

198 

206 

214 

223 

231 

240 

248 

257 



516 

265 

273 

282 

290 

299 

307 

315 

324 

332 

341 



517 

349 

357 

366 

374 

383 

391 

399 

408 

416 

425 



518 

433 

441 

450 

458 

466 

475 

483 

492 

,500 

508 



519 

517 

525 

533 

542 

550 

559 

567 

575 

584 

592 



520 

600 

609 

617 

625 

634 

642 

650 

659 

667 

675 



521 

684 

692 

700 

709 

717 

725 

734 

742 

750 

759 


g 

522 

767 

775 

784 

792 

800 

809 

817 

825 

834 

842 



523 

850 

858 

867 

875 

883 

892 

900 

908 

917 

925 

1 

0.8 

524 

933 

941 

950 

958 

966 

975 

983 

991 

999 

*008 

2 

1.6 












3 

2.4 

525 

72 016 

024 

032 

041 

049 

057 

066 

074 

082 

090 

4 

3.2 

4.0 

4 8 

526 

099 

107 

115 

123 

132 

140 

148 

156 

165 

173 

5 

Q 

527 

181 

189 

198 

206 

214 

222 

230 

239 

247 

255 

7 

5^6 

528 

263 

272 

280 

288 

296 

304 

313 

321 

329 

337 

8 

6.4 

529 

346 

354 

362 

370 

378 

387 

395 

403 

411 

419 

9 

7.2 

530 

428 

436 

444 

452 

460 

469 

477 

485 

493 

501 



531 

509 

518 

526 

534 

542 

550 

558 

567 

575 

583 



532 

591 

599 

607 

616 

624 

632 

640 

648 

656 

665 



533 

673 

681 

689 

697 

705 

713 

722 

730 

738 

746 



534 

754 

762 

770 

779 

787 

795 

803 

811 

819 

827 



535 

835 

843 

852 

860 

868 

876 

884 

892 

900 

908 



536 

916 

925 

933 

941 

949 

957 

965 

973 

981 

989 



537 

997 

*006 

*014 

*022 

*030 

*038 

*046 

*054 

*062 

*070 


7 

538 

73 078 

086 

094 

102 

111 

119 

127 

135 

143 

151 

1 

2 

0.7 

1.4 

2.1 

2.8 

539 

159 

167 

175 

183 

191 

199 

207 

215 

223 

231 

540 

239 

247 

255 

263 

272 

280 

288 

296 

304 

312 

3 

4 

541 

320 

328 

336 

344 

352 

360 

368 

376 

384 

392 

5 

3.5 

4.2 

4.9 

542 

400 

408 

416 

424 

432 

440 

448 

456 

464 

472 

O 

7 

543 

480 

488 

496 

504 

512 

520 

528 

536 

544 

552 

8 

5.6 

544 

560 

568 

576 

584 

592 

600 

608 

616 

624 

632 

9 

6.3 i 

545 

640 

648 

656 

664 

672 

679 

687 

695 

703 

711 



546 

719 

727 

735 

743 

751 

759 

767 

775 

783 

791 



547 

799 

807 

815 

823 

830 

838 

846 

854 

862 

870 



548 

878 

886 

894 

902 

910 

918 

926 

933 

941 

949 



549 

957 

965 

973 

981 

989 

997 

*005 

*013 

*020 

*028 



550 

74 036 

044 

052 

060 

068 

076 

084 

092 

099 

107 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. ' 





































VII 


FIVE-PLACE LOGARITHMS' OF NUMBERS 


83 


660-600 


N 

L 0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Prop. Pts. 

550 

74 036 

044 

052 

060 

068 

076 

084 

092 

099 

107 



551 

115 

123 

131 

139 

147 

155 

162 

170 

178 

186 



552 

194 

202 

210 

218 

225 

233 

241 

249 

257 

265 



553 

273 

280 

288 

296 

304 

312 

320 

327 

335 

343 



554 

351 

359 

367 

374 

382 

390 

398 

406 

414 

421 



555 

429 

437 

445 

453 

461 

468 

476 

484 

492 

500 



556 

507 

515 

523 

531 

539 

547 

554 

562 

570 

578 



557 

586 

593 

601 

609 

617 

624 

632 

640 

648 

656 



558 

663 

671 

679 

687 

695 

702 

710 

718 

726 

733 



559 

741 

749 

757 

764 

772 

780 

788 

796 

803 

811 



560 

819 

827 

834 

842 

850 

858 

865 

873 

881 

889 



561 

896 

904 

912 

920 

927 

935 

943 

950 

958 

966 


8 

562 

974 

981 

989 

997 

*005 

*012 

*020 

*028 

*035 

*043 



563 

75 051 

059 

066 

074 

082 

089 

097 

105 

113 

120 

1 

0.8 

564 

128 

136 

143 

151 

159 

166 

174 

182 

189 

197 

2 

3 

1.6 

2.4 












4 

3.2 

565 

205 

213 

220 

228 

236 

243 

251 

259 

266 

274 

5 

4.0 

566 

282 

289 

297 

305 

312 

320 

328 

335 

343 

351 

6 

4.8 

567 

358 

366 

374 

381 

389 

397 

404 

412 

420 

427 

7 

Q 

6.6 

568 

435 

442 

450 

458 

465 

473 

481 

488 

496 

504 

O 

9 

•7!2 

569 

511 

519 

526 

534 

542 

549 

557 

565 

572 

580 



570 

587 

595 

603 

610 

618 

626 

633 

641 

648 

656 



571 

664 

671 

679 

686 

694 

702 

709 

717 

724 

732 



572 

740 

747 

755 

762 

770 

778 

785 

793 

800 

808 



573 

815 

823 

831 

838 

846 

853 

861 

868 

876 

884 



574 

891 

899 

906 

914 

921 

929 

937 

944 

952 

959 



575 

967 

974 

982 

989 

997 

*005 

*012 

*020 

*027 

*035 



576 

76 042 

050 

057 

065 

072 

080 

087 

095 

103 

110 



577 

118 

125 

133 

140 

148 

155 

163 

170 

178 

185 



578 

193 

200 

208 

215 

223 

230 

238 

245 

253 

260 



579 

268 

275 

283 

290 

298 

305 

313 

320 

328 

335 



580 

343 

350 

358 

365 

373 

380 

388 

395 

403 

410 



581 

418 

425 

433 

440 

448 

455 

462 

470 

477 

485 



582 

492 

500 

507 

515 

522 

530 

537 

545 

552 

559 


7 

583 

567 

574 

582 

589 

597 

604 

612 

619 

626 

634 

1 

rt 7 

584 

641 

649 

656 

664 

671 

678 

686 

693 

701 

708 

1 

2 

U . i 

1.4 












3 

2.1 

585 

716 

723 

730 

738 

745 

753 

760 

768 

775 

782 

4 

2.8 

586 

790 

797 

805 

812 

819 

827 

834 

842 

849 

856 

5 

3.5 

587 

864 

871 

879 

886 

893 

901 

908 

916 

923 

930 

6 

7 

4.2 

A. Q 

588 

938 

945 

953 

960 

867 

975 

982 

989 

997 

*004 

i 

8 

6.6 

589 

77 012 

019 

026 

034 

041 

048 

056 

063 

070 

078 

9 

6.3 

590 

085 

093 

100 

107 

115 

122 

129 

137 

144 

151 



591 

159 

166 

173 

181 

188 

195 

203 

210 

217 

225 



592 

232 

240 

247 

254 

262 

269 

276 

283 

291 

298 



593 

305 

313 

320 

327 

335 

342 

349 

357 

364 

371 



594 

379 

386 

393 

401 

408 

415 

422 

430 

437 

444 



595 

452 

459 

466 

474 

481 

488 

495 

503 

510 

517 



596 

525 

532 

539 

546 

554 

561 

568 

576 

583 

590 



597 

597 

605 

612 

619 

627 

634 

641 

648 

656 

663 



598 

670 

677 

685 

692 

699 

706 

714 

721 

728 

735 



599 

743 

750 

757 

764 

772 

779 

786 

793 

801 

808 



600 

815 

822 

830 

837 

844 

851 

859 

866 

873 

880 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 










































































84 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


600-650 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

600 

77 815 

822 

830 

837 

844 

851 

859 

866 

873 

880 



601 

887 

895 

902 

909 

916 

924 

931 

938 

945 

952 



602 

960 

967 

974 

981 

988 

996 

*003 

*010 

*017 

*025 



603 

78 032 

039 

046 

053 

061 

068 

075 

082 

089 

097 



604 

104 

111 

118 

1.25 

132 

140 

147 

154 

161 

168 



605 

176 

183 

190 

197 

204 

211 

219 

226 

233 

240 



606 

247 

254 

262 

269 

276 

283 

290 

297 

305 

312 


s 

607 

319 

326 

333 

340 

347 

355 

362 

369 

376 

383 



608 

390 

398 

405 

412 

419 

426 

433 

440 

447 

455 

1 

0.8 

609 

462 

469 

476 

483 

490 

497 

504 

512 

519 

526 

2 

3 

1.6 

2.4 

610 

533 

540 

547 

554 

561 

569 

576 

583 

590 

597 

4 

5 

3.2 

4.0 

4.8 

611 

604 

611 

618 

625 

633 

640 

647 

654 

661 

668 

6 

612 

675 

682 

689 

696 

704 

711 

718 

725 

732 

739 

7 

5.6 

613 

746 

753 

760 

767 

774 

781 

789 

796 

803 

810 

8 

6.4 

614 

817 

824 

831 

838 

845 

852 

859 

866 

873 

880 

9 

7.2 

615 

888 

895 

902 

909 

916 

923 

930 

937 

944 

951 



616 

958 

965 

972 

979 

986 

993 

*000 

*007 

*014 

*021 



617 

79 029 

036 

043 

050 

057 

064 

071 

078 

085 

092 



618 

099 

106 

113 

120 

127 

134 

141 

148 

155 

162 



619 

169 

176 

183 

190 

197 

204 

211 

218 

225 

232 



620 

239 

246 

253 

260 

267 

274 

281 

^288 

295 

302 



621 

309 

316 

323 

330 

337 

344 

351 

358 

365 

372 


IT 

622 

379 

386 

393 

400 

407 

414 

421 

428 

435 

442 


f 

623 

449 

456 

463 

470 

477 

484 

491 

498 

505 

511 

1 

0.7 

624 

518 

525 

532 

539 

546 

553 

560 

567 

574 

581 

2 

3 

1.4 

2.1 

2.8 

3.5 

4 2 

625 

588 

595 

602 

609 

616 

623 

630 

637 

644 

650 

4 

626 

657 

664 

671 

678 

685 

692 

699 

706 

713 

720 

5 

g 

627 

727 

734 

741 

748 

754 

761 

768 

775 

782 

789 

7 

4^9 

628 

796 

803 

810 

817 

824 

831 

837 

844 

851 

858 

8 

5.6 

629 

865 

872 

879 

886 

893 

900 

906 

913 

920 

927 

9 

6.3 

630 

934 

941 

948 

955 

962 

969 

975 

982 

989 

996 



631 

80 003 

010 

017 

024 

030 

037 

044 

051 

058 

065 



632 

072 

079 

085 

092 

099 

106 

113 

120 

127 

134 



633 

140 

147 

154 

161 

168 

175 

182 

188 

195 

202 



634 

209 

216 

223 

229 

236 

243 

250 

257 

264 

271 



635 

277 

284 

291 

298 

305 

312 

318 

325 

332 

339 



636 

346 

353 

359 

366 

373 

380 

387 

393 

400 

407 



637 

414 

421 

428 

434 

441 

448 

455 

462 

468 

475 


6 

638 

482 

489 

496 

502 

509 

516 

523 

530 

536 

543 

1 

2 

0.6 

1.2 

1.8 

2.4 

639 

550 

557 

564 

570 

577 

584 

591 

598 

604 

611 

640 

618 

625 

632 

638 

645 

652 

659 

665 

672 

679 

3 

4 

641 

686 

693 

699 

706 

713 

720 

726 

733 

740 

747 

5 

6 

7 

3.0 

3.6 

4.2 

4.8 

642 

754 

760 

767 

774 

781 

787 

794 

801 

808 

814 

643 

821 

828 

835 

841 

848 

855 

862 

868 

875 

882 

8 

644 ' 

889 

895 

902 

909 

916 

922 

929 

936 

943 

949 

9 

5.4 

645 

956 

963 

969 

976 

983 

990 

996 

*003 

*010 

*017 



646 

81 023 

030 

037 

043 

050 

057 

064 

070 

077 

084 



647 

090 

097 

104 

111 

117 

124 

131 

137 

144 

151 



648 

158 

164 

171 

178 

184 

191 

198 

204 

211 

218 



649 

224 

231 

238 

245 

251 

258 

265 

271 

278 

285 



650 

291 

298 

305 

311 

318 

325 

331 

338 

345 

351 



N 

L 0 

1 

2 

3 

4 

5 

6 • 

7 

8 

9 

Prop. Pts. 








































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


85 


650-700 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

650 

81 291 

298 

305 

311 

318 

325 

331 

338 

345 

351 



651 

358 

365 

371 

378 

385 

391 

398 

405 

411 

418 



652 

425 

431 

438 

445 

451 

458 

465 

471 

478 

485 



653 

491 

498 

505 

511 

518 

525 

531 

538 

544 

551 



654 

558 

564 

571 

578 

584 

591 

598 

604 

611 

617 



655 

624 

631 

637 

644 

651 

657 

664 

671 

677 

684 



656 

690 

697 

704 

710 

717 

723 

730 

737 

743 

750 



657 

757 

763 

770 

776 

783 

790 

796 

803 

809 

816 



658 

823 

829 

836 

842 

849 

856 

862 

869 

875 

882 



659 

889 

895 

902 

908 

915 

921 

928 

935 

941 

948 



660 

954 

961 

968 

974 

981 

987 

994 

*000 

*007 

*014 



661 

82 020 

027 

033 

040 

046 

053 

060 

066 

073 

079 


7 

662 

086 

092 

099 

105 

112 

119 

125 

132 

138 

145 



663 

151 

158 

164 

171 

178 

184 

191 

197 

204 

210 

1 

0.7 

664 

217 

223 

230 

236 

243 

249 

256 

263 

269 

276 

2 

3 

1.4 

2.1 

665 

282 

289 

295 

302 

308 

315 

321 

328 

334 

341 

4 

5 

2.8 

3.5 

666 

347 

354 

360 

367 

373 

380 

387 

393 

400 

406 

6 

4.2 

667 

413 

419 

426 

432 

439 

445 

452 

458 

465 

471 

7 

4.9 

668 

478 

484 

491 

497 

504 

510 

517 

523 

530 

536 

8 

Q 

5.6 

6.3 

669 

543 

549 

556 

562 

569 

575 

582 

588 

595 

601 


670 

607 

614 

620 

627 

633 

640 

646 

653 

659 

666 



671 

672 

679 

685 

692 

698 

705 

711 

718 

724 

730 



672 

737 

743 

750 

756 

763 

769 

776 

782 

789 

795 



673 

802 

808 

814 

821 

827 

834 

840 

847 

853 

860 



674 

866 

872 

879 

885 

892 

898 

905 

911 

918 

924 



675 

930 

937 

943 

950 

956 

963 

969 

975 

982 

988 



676 

995 

*001 

*008 

*014 

*020 

*027 

*033 

*040 

*046 

*052 



677 

83 059 

065 

072 

078 

085 

091 

097 

104 

no 

117 



678 

123 

129 

136 

142 

149 

155 

161 

168 

174 

181 



679 

187 

193 

200 

206 

213 

219 

225 

232 

238 

245 



680 

251 

257 

264 

270 

276 

283 

289 

296 

302 

308 



681 

315 

321 

327 

334 

340 

347 

353 

359 

366 

372 



682 

378 

385 

391 

398 

404 

410 

417 

423 

429 

436 


6 

683 

442 

448 

455 

461 

467 

474 

480 

487 

493 

499 

1 

2 

0.6 

1.2 

684 

506 

512 

518 

525 

531 

537 

544 

550 

556 

563 












3 

1.8 

685 

569 

575 

582 

588 

594 

601 

607 

613 

620 

626 

4 

2.4 

686 

632 

639 

645 

651 

658 

664 

670 

677 

683 

689 

5 

3.0 

687 

696 

702 

708 

715 

721 

727 

734 

740 

746 

753 

6 

3.6 

4.2 

4 8 

688 

759 

765 

771 

778 

784 

790 

797 

803 

809 

816 

7 

8 

689 

822 

828 

835 

841 

847 

853 

860 

866 

872 

879 

9 

5.4 

690 

885 

891 

897 

904 

910 

916 

923 

929 

935 

942 



691 

948 

954 

960 

967 

973 

979 

985 

992 

998 

*004 



692 

84 011 

017 

023 

029 

036 

042 

048 

055 

061 

067 



693 

073 

080 

086 

092 

098 

105 

111 

117 

123 

130 



694 

136 

142 

148 

155 

161 

167 

173 

180 

186 

192 



695 

198 

205 

211 

217 

223 

230 

236 

242 

248 

255 



696 

261 

267 

273 

280 

286 

292 

298 

305 

311 

317 



697 

323 

330 

336 

342 

348 

354 

361 

367 

373 

379 



698 

386 

392 

398 

404 

410 

417 

423 

429 

435 

442 



699 

448 

454 

460 

466 

473 

479 

485 

491 

497 

504 



700 

510 

516 

522 

528 

535 

541 

547 

553 

559 

566 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

1 

8 

9 

Prop. Pts. 























































86 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


700-750 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

700 

84 510 

516 

522 

528 

535 

541 

547 

553 

559 

566 



701 

572 

578 

584 

590 

597 

603 

609 

615 

621 

628 



702 

634 

640 

646 

652 

658 

665 

671 

677 

683 

689 



703 

696 

702 

708 

714 

720 

726 

733 

739 

745 

751 



704 

757 

763 

770 

776 

782 

788 

794 

800 

807 

813 



705 

819 

825 

831 

837 

844 

850 

856 

862 

868 

874 



706 

880 

887 

893 

899 

905 

911 

917 

924 

930 

936 


7 

707 

942 

948 

954 

960 

967 

973 

979 

985 

991 

997 



708 

85 003 

009 

016 

022 

028 

034 

040 

046 

052 

058 

1 

0.7 

709 

065 

071 

077 

083 

089 

095 

101 

107 

114 

120 

2 

3 

1.4 

2.1 

710 

126 

132 

138 

144 

150 

156 

163 

169 

175 

181 

4 

5 

2.8 

3.5 

711 

187 

193 

199 

205 

211 

217 

224 

230 

236 

242 

6 

4.2 

712 

248 

254 

260 

266 

272 

278 

285 

291 

297 

303 

7 

4.9 

713 

309 

315 

321 

327 

333 

339 

345 

352 

358 

364 

8 

Q 

5.6 

714 

370 

376 

382 

388 

394 

400 

406 

412 

418 

425 


u.o 

715 

431 

437 

443 

449 

455 

461 

467 

473 

479 

485 



716 

491 

497 

503 

509 

516 

522 

528 

534 

540 

546 



717 

552 

558 

564 

570 

576 

582 

588 

594 

600 

606 



718 

612 

618 

625 

631 

637 

643 

649 

655 

661 

667 



719 

673 

679 

685 

691 

697 

703 

709 

715 

721 

727 



720 

733 

739 

745 

751 

757 

763 

769 

775 

781 

788 



721 

794 

800 

806 

812 

818 

824 

830 

836 

842 

848 


0 

722 

854 

860 

866 

872 

878 

884 

890 

896 

902 

908 



723 

914 

920 

926 

932 

938 

944 

950 

956 

962 

968 

1 

0.6 

724 

974 

980 

986 

992 

998 

*004 

*010 

*016 

*022 

*028 

2 

1.2 












3 

1.8 

725 

86 034 

040 

046 

052 

058 

064 

070 

076 

082 

088 

. 4 

5 

2.4 

3 0 

726 

094 

100 

106 

112 

118 

124 

130 

136 

141 

147 

6 

3.6 

727 

153 

159 

165 

171 

177 

183 

189 

195 

201 

207 

7 

4.2 

728 

213 

219 

225 

231 

237 

243 

249 

255 

261 

267 

8 

4.8 

729 

273 

279 

285 

291 

297 

303 

308 

314 

320 

326 

9 

5.4 

730 

332 

338 

344 

350 

356 

362 

368 

374 

380 

386 



731 

392 

398 

404 

410 

415 

421 

427 

433 

439 

445 



732 

451 

457 

463 

469 

475 

481 

487 

493 

499 

504 



733 

510 

516 

522 

528 

534 

540 

546 

552 

558 

564 



734 

570 

576 

581 

587 

593 

599 

605 

611 

617 

623 



735 

629 

635 

641 

646 

652 

658 

664 

670 

676 

682 



736 

688 

694 

700 

705 

711 

717 

723 

729 

735 

741 



737 

747 

753 

759 

764 

770 

776 

782 

788 

794 

800 


5 

738 

806 

812 

817 

823 

829 

835 

841 

847 

853 

859 

1 

0 5 

739 

864 

870 

876 

882 

888 

894 

900 

906 

911 

917 

2 

i!o 












Q 

1 5 

740 

923 

929 

935 

941 

947 

953 

958 

964 

970 

976 

o 

4 

2.0 

741 

982 

988 

994 

999 

*005 

*011 

*017 

*023 

*029 

*035 

5 

0 

2.5 

3 0 

742 

87 040 

046 

052 

058 

064 

070 

075 

081 

087 

093 

7 

3.5 

743 

099 

105 

111 

116 

122 

128 

134 

140 

146 

151 

8 

4.0 

744 

157 

163 

169 

175 

181 

186 

192 

198 

204 

210 

9 

4.5 

745 

216 

221 

227 

233 

239 

245 

251 

256 

262 

268 



746 

274 

280 

286 

291 

297 

303 

309 

315 

320 

326 



747 

332 

338 

344 

349 

355 

361 

367 

373 

379 

384 



748 

390 

396 

402 

408 

413 

419 

425 

431 

437 

442 



749 

448 

454 

460 

466 

471 

477 

483 

489 

495 

500 



760 

506 

512 

518 

523 

529 

535 

541 

547 

552 

558 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 














































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


87 


750-800 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

750 

87 506 

512 

518 

523 

529 

535 

541 

547 

552 

558 



751 

564 

570 

576 

581 

587 

593 

599 

604 

610 

616 



752 

622 

628 

633 

639 

645 

651 

656 

662 

668 

674 



753 

679 

685 

691 

697 

703 

708 

714 

720 

726 

731 



754 

737 

743 

749 

754 

760 

766 

772 

777 

783 

789 



755 

795 

800 

806 

812 

818 

823 

829 

835 

841 

846 



756 

852 

858 

864 

869 

875 

881 

887 

892 

898 

904 



757 

910 

915 

921 

927 

933 

938 

944 

950 

955 

961 



758 

967 

973 

978 

984 

990 

996 

*001 

*007 

*013 

*018 



759 

88 024 

030 

036 

041 

047 

053 

058 

064 

070 

076 



760 

081 

087 

093 

098 

104 

110 

116 

121 

127 

133 



761 

138 

144 

150 

156 

161 

167 

173 

178 

184 

190 


6 

762 

195 

201 

207 

213 

218 

224 

230 

235 

241 

247 



763 

252 

258 

264 

270 

275 

281 

287 

292 

298 

304 

1 

0.6 

764 

309 

315 

321 

326 

332 

338 

343 

349 

355 

360 

3 

1.8 












4 

2.4 

765 

366 

372 

377 

383 

389 

395 

400 

406 

412 

417 

5 

3.0 

766 

423 

429 

434 

440 

446 

451 

457 

463 

468 

474 

6 

3.6 

767 

480 

485 

491 

497 

502 

508 

513 

519 

525 

530 

7 

4.2 

A e 

768 

536 

542 

547 

553 

559 

564 

570 

576 

581 

587 

9 

5.4 

769 

593 

598 

604 

610 

615 

621 

627 

632 

638 

643 



770 

649 

655 

660 

666 

672 

677 

683 

689 

694 

700 



771 

705 

711 

717 

722 

728 

734 

739 

745 

750 

756 



772 

762 

767 

773 

779 

784 

790 

795 

801 

807 

812 



773 

818 

824 

829 

835 

840 

846 

852 

857 

863 

868 



774 

874 

880 

885 

891 

897 

902 

908 

913 

919 

925 



775 

930 

936 

941 

947 

953 

958 

964 

969 

975 

981 



776 

986 

992 

997 

*003 

*009 

*014 

*020 

*025 

*031 

*037 



777 

89 042 

048 

053 

059 

064 

070 

076 

081 

087 

092 



778 

098 

104 

109 

115 

120 

126 

131 

137 

143 

148 



779 

154 

159 

165 

170 

176 

182 

187 

193 

198 

204 



780 

209 

215 

221 

226 

232 

237 

243 

248 

254 

260 



781 

265 

271 

276 

282 

287 

293 

298 

304 

310 

315 



782 

321 

326 

332 

337 

343 

348 

354 

360 

365 

371 


6 

783 

376 

382 

387 

393 

398 

404 

409 

415 

421 

426 

1 

0 5 

784 

432 

437 

443 

448 

454 

459 

465 

470 

476 

481 

2 

i.’o 












3 

1.5 

785 

487 

492 

498 

504 

509 

515 

520 

526 

531 

537 

4 

2.0 

786 

542 

548 

553 

559 

564 

570 

575 

581 

586 

592 

5 

2^5 

O A 

787 

597 

603 

609 

614 

620 

625 

631 

636 

642 

647 

6 

7 

o.U 

3 5 

788 

653 

658 

664 

669 

675 

680 

686 

691 

697 

702 

8 

4!o 

789 

708 

713 

719 

724 

730 

735 

741 

746 

752 

757 

9 

4.5 

790 

763 

768 

774 

779 

785 

790 

796 

801 

807 

812 



791 

818 

823 

829 

834 

840 

845 

851 

856 

862 

867 



792 

873 

878 

883 

889 

894 

900 

905 

911 

916 

922 



793 

927 

933 

938 

944 

949 

955 

960 

966 

971 

977 



794 

982 

988 

993 

998 

*004 

*009 

*015 

*020 

*026 

*031 



795 

90 037 

042 

048 

053 

059 

064 

069 

075 

080 

086 



796 

091 

097 

102 

108 

113 

119 

124 

129 

135 

140 



797 

146 

151 

157 

162 

168 

173 

179 

184 

189 

195 



798 

200 

206 

211 

217 

222 

227 

233 

238 

244 

249 



799 

255 

260 

266 

271 

276 

282 

287 

293 

298 

304 



800 

309 

314 

320 

325 

331 

33^ 

342 

347 

352 

358 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 



























































88 - 


five-place LOGARITHMS OF NUMBERS 


vn 


800-850 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

1 

8 

9 

Prop. Pts. 

800 

90 309 

314 

320 

325 

331 

336 

342 

347 

352 

358 



801 

363 

369 

374 

380 

385 

390 

396 

401 

407 

412 



802 

417 

423 

428 

434 

439 

445 

450 

455 

461 

466 



803 

472 

477 

482 

488 

493 

499 

504 

509 

515 

520 



804 

526 

531 

536 

542 

547 

553 

558 

563 

569 

574 



805 

580 

585 

590 

596 

601 

607 

612 

617 

623 

628 



806 

634 

639 

644 

650 

655 

660 

666 

671 

677 

682 



807 

687 

693 

698 

703 

709 

714 

720 

725 

730 

736 



808 

741 

747 

752 

757 

763 

768 

773 

779 

784 

789 



809 

795 

800 

806 

811 

816 

822 

827 

832 

838 

843 



810 

849 

854 

859 

865 

870 

875 

881 

886 

891 

897 



811 

902 

907 

913 

918 

924 

929 

934 

940 

945 

950 


6 

812 

956 

961 

966 

972 

977 

982 

988 

993 

998 

*004 



813 

91 009 

014 

020 

025 

030 

036 

041 

046 

052 

057 

1 

9 

0.6 

7 9 

814 

062 

068 

073 

078 

084 

089 

094 

100 

105 

110 

3 

X .A 

1.8 












4 

2.4 

815 

116 

121 

126 

132 

137 

142 

148 

153 

158 

164 

5 

3.0 

816 

169 

174 

180 

185 

190 

196 

201 

206 

212 

217 

6 

3.6 

817 

222 

228 

233 

238 

243 

249 

254 

259 

265 

270 

7 

o 

4.2 

A Q 

818 

275 

281 

286 

291 

297 

302 

307 

312 

318 

323 

O 

9 

•±.8 

5.4 

819 

328 

334 

339 

344 

350 

355 

360 

365 

371 

376 



820 

381 

387 

392 

397 

403 

408 

413 

418 

424 

429 



821 

434 

440 

445 

450 

455 

461 

466 

471 

477 

482 



822 

487 

492 

498 

503 

508 

514 

519 

524 

529 

535 



823 

540 

545 

551 

556 

561 

566 

572 

577 

582 

587 



824 

593 

598 

603 

609 

614 

619 

624 

630 

635 

640 



825 

645 

651 

656 

661 

666 

672 

677 

682 

687 

693 



826 

698 

703 

709 

714 

719 

724 

730 

735 

740 

745 



827 

751 

756 

761 

766 

772 

777 

782 

787 

793 

798 



828 

803 

808 

814 

819 

824 

829 

834 

840 

845 

850 



829 

855 

861 

866 

871 

876 

882 

887 

892 

897 

903 



830 

908 

913 

918 

924 

929 

934 

939 

944 

950 

955 



831 

960 

965 

971 

976 

981 

986 

991 

997 

*002 

*007 



832 

92 012 

018 

023 

028 

033 

038 

044 

049 

054 

059 


5 

833 

065 

070 

075 

080 

085 

091 

096 

101 

106 

111 

1 


834 

117 

122 

127 

132 

137 

143 

148 

153 

158 

163 

L 

2 

0 5 

i!o 












3 

1.5 

835 

169 

174 

179 

184 

189 

195 

200 

205 

210 

215 

4 

2.0 

836 

221 

226 

231 

236 

241 

247 

252 

257 

262 

267 

5 

2.5 

837 

273 

278 

283 

288 

293 

298 

304 

309 

314 

319 

6 

7 

3.0 

838 

324 

330 

335 

340 

345 

350 

355 

361 

366 

371 

4 

8 

0.0 

4.0 

839 

376 

381 

387 

392 

397 

402 

407 

412 

418 

423 

9 

4.5 

840 

428 

433 

438 

443 

449 

454 

459 

464 

469 

474 



841 

480 

485 

490 

495 

500 

505 

511 

516 

521 

526 



842 

531 

536 

542 

547 

552 

557 

562 

567 

572 

578 



843 

583 

588 

593 

598 

603 

609 

614 

619 

624 

629 



844 

634 

639 

645 

650 

655 

660 

665 

670 

675 

681 



845 

686 

691 

696 

701 

706 

711 

716 

722 

727 

732 



846 

737 

742 

747 

752 

758 

763 

768 

773 

778 

783 



847 

788 

793 

799 

804 

809 

814 

819 

824 

829 

834 



848 

840 

845 

850 

855 

860 

865 

870 

875 

881 

886 



849 

891 

896 

901 

906 

911 

916 

921 

927 

932 

937 



850 

942 

947 

952 

957 

962 

967 

973 

978 

983 

988 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 







































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


89 


850-900 


N 

L 0 

1 

2 

3 

4 

6 

6 

7 

8 

9 

Prop. Pts. 

850 

92 942 

947 

952 

957 

962 

967 

973 

978 

983 

988 



851 

993 

998 

*003 

*008 

*013 

*018 

*024 

*029 

*034 

*039 



852 

93 044 

049 

054 

059 

064 

069 

075 

080 

085 

090 



853 

095 

100 

105 

no 

115 

120 

125 

131 

181 

141 



854 

146 

151 

156 

161 

166 

171 

176 

181 

186 

192 



855 

197 

202 

207 

212 

217 

222 

227 

232 

237 

242 



856 

247 

252 

258 

263 

268 

273 

278 

283 

288 

293 


6 

857 

298 

303 

308 

313 

318 

323 

328 

334 

339 

344 



858 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

1 

0.6 

859 

399 

404 

409 

414 

420 

425 

430 

435 

440 

445 

2 

1.2 












3 

1.8 

860 

450 

455 

460 

465 

470 

475 

480 

485 

490 

495 

4 

5 

2.4 

3.0 

861 

500 

505 

510 

515 

520 

526 

531 

536 

541 

546 

6 

3.6 

862 

551 

556 

561 

566 

571 

576 

581 

586 

591 

596 

7 

4.2 

863 

601 

606 

611 

616 

621 

626 

631 

636 

641 

646 

8 

Q 

4.8 

5.4 

864 

651 

656 

661 

666 

671 

676 

682 

687 

692 

697 


865 

702 

707 

712 

717 

722 

727 

732 

737 

742 

747 



866 

752 

757 

762 

767 

772 

777 

782 

787 

792 

797 



867 

802 

807 

812 

817 

822 

827 

832 

837 

842 

847 



868 

852 

857 

862 

867 

872 

877 

882 

887 

892 

897 



869 

902 

907 

912 

917 

922 

927 

932 

937 

942 

947 



870 

952 

957 

962 

967 

972 

977 

982 

987 

992 

997 



871 

94 002 

007 

012 

017 

022 

027 

032 

037 

042 

047 


5 

872 

052 

057 

062 

067 

072 

077 

082 

086 

091 

096 



873 

101 

106 

111 

116 

121 

126 

131 

136 

141 

146 

1 

0.5 

874 

151 

156 

161 

166 

171 

176 

181 

186 

191 

196 

2 

3 

1.0 

1.5 

875 

201 

206 

211 

216 

221 

226 

231 

236 

240 

245 

4 

5 

2.0 

2 5 

876 

250 

255 

260 

265 

270 

275 

280 

285 

290 

295 

6 

3.0 

877 

300 

305 

310 

315 

320 

325 

330 

335 

340 

345 

7 

3.5 

878 

349 

354 

359 

364 

369 

374 

379 

384 

389 

394 

8 

4.0 

879 

399 

404 

409 

414 

419 

424 

429 

433 

438 

443 

9 

4.5 

880 

448 

453 

458 

463 

468 

473 

478 

483 

488 

493 



881 

498 

503 

507 

512 

517 

522 

527 

532' 

537 

542 



882 

547 

552 

557 

562 

567 

571 

576 

581 

586 

591 



883 

596 

601 

606 

611 

616 

621 

626 

630 

635 

640 



884 

645 

650 

655 

660 

665 

670 

675 

680 

685 

689 



885 

694 

699 

704 

709 

714 

719 

724 

729 

734 

738 



886 

743 

748 

753 

758 

763 

768 

773 

778 

783 

787 



887 

792 

797 

802 

807 

812 

817 

822 

827 

832 

836 



888 

841 

846 

851 

856 

861 

866 

871 

876 

880 

885 

1 

0.4 

889 

890 

895 

900 

905 

910 

915 

919 

924 

929 

934 

2 

0.8 











3 

1.2 

890 

939 

944 

949 

954 

959 

963 

968 

973 

978 

983 

4 

5 

1.6 

2 0 

891 

988 

993 

998 

*002 

*007 

*012 

*017 

*022 

*027 

*032 

6 

2^4 

892 

95 036 

041 

046 

051 

056 

061 

066 

071 

075 

080 

7 

2.8 

893 

085 

090 

095 

100 

105 

109 

114 

119 

124 

129 

8 

3.2 

894 

134 

139 

143 

148 

153 

158 

163 

168 

173 

177 

9 

3.6 

895 

182 

187 

192 

197 

202 

207 

211 

216 

221 

226 



896 

231 

236 

240 

245 

250 

255 

260 

265 

270 

274 



897 

279 

284 

289 

294 

299 

303 

308 

313 

318 

323 



898 

328 

332 

337 

342 

347 

352 

357 

361 

366 

371 



899 

376 

381 

386 

390 

395 

400 

405 

410 

415 

419 



900 

424 

429 

434 

439 

444 

448 

453 

458 

463 

468 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 







































































90 


FIVE-PLACE LOGARITHMS OF NUMBERS 


VII 


900-950 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

T - 

9 

Prop. Pts. 

900 

95 424 

429 

434 

439 

444 

448 

453 

458 

463 

468 



901 

472 

477 

482 

487 

492 

497 

501 

506 

511 

516 



902 

521 

525 

530 

535 

540 

545 

550 

554 

559 

564 



903 

569 

574 

578 

583 

588 

593 

598 

602 

607 

612 



904 

617 

622 

626 

631 

636 

641 

646 

650 

655 

660 



905 

665 

670 

674 

679 

684 

689 

694 

698 

703 

708 



906 

713 

718 

722 

727 

732 

737 

742 

746 

751 

756 



907 

761 

766 

770 

775 

780 

785 

789 

794 

799 

804 



908 

809 

813 

818 

823 

828 

832 

837 

842 

847 

852 



909 

856 

861 

866 

871 

875 

880 

885 

890 

895 

899 



910 

904 

909 

914 

018 

923 

928 

933 

938 

942 

947 



911 

952 

957 

961 

966 

971 

976 

980 

985 

990 

995 


5 

912 

999 

*004 

*009 

*014 

*019 

*023 

*028 

*033 

*038 

*042 

1 

o 

0.5 

1.0 

1.5 

913 

96 047 

052 

057 

061 

066 

071 

076 

080 

085 

090 

914 

095 

099 

104 

109 

114 

118 

123 

128 

133 

137 

3 

915 

142 

147 

152 

156 

161 

166 

171 

175 

180 

185 

4 

5 

2.0 

2.5 

916 

190 

194 

199 

204 

209 

213 

218 

223 

227 

232 

6 

3.0 

917 

237 

242 

246 

251 

256 

261 

265 

270 

275 

280 

7 

3.5 

918 

284 

289 

294 

298 

303 

308 

313 

317 

322 

327 

8 

9 

4.0 

4.5 

919 

332 

336 

341 

346 

350 

355 

360 

365 

369 

374 


920 

379 

384 

388 

393 

398 

402 

407 

412 

417 

421 



921 

426 

431 

435 

440 

445 

450 

454 

459 

464 

468 



922 

473 

478 

483 

487 

492 

497 

501 

506 

511 

515 



923 

520 

525 

530 

534 

539 

544 

548 

553 

558 

562 



924 

567 

572 

577 

581 

586 

591 

595 

600 

605 

609 



925 

614 

619 

624 

628 

633 

638 

642 

647 

652 

656 



926 

661 

666 

670 

675 

680 

685 

689 

694 

699 

703 



927 

708 

713 

717 

722 

727 

731 

736 

741 

745 

750 



928 

755 

759 

764 

769 

774 

778 

783 

788 

792 

797 



929 

802 

806 

811 

816 

820 

825 

830 

834 

839 

844 



930 

848 

853 

858 

862 

876 

872 

876 

881 1 

886 

890 



931 

895 

900 

904 

909 

914 

918 

923 

928 

932 

937 



932 

942 

946 

951 

956 

960 

965 

970 

974 

979 

984 


4 

933 

988 

993 

997 

*002 

*007 

*011 

*016 

*021 

*025 

*030 

1 

2 

0.4 

0.8 

934 

97 035 

039 

044 

049 

053 

058 

063 

067 

072 

077 

935 

081 

086 

090 

095 

100 

104 

109 

114 

118 

123 

3 

4 

1.2 

1.6 

936 

128 

132 

137 

142 

146 

151 

155 

160 

165 

169 

5 

2.0 

937 

174 

179 

183 

188 

192 

197 

202 

206 

211 

216 

6 

2.4 

938 

220 

225 

230 

234 

239 

243 

248 

253 

257 

262 

7 

g 

2.8 

3.2 

3.6 

939 

267 

271 

276 

280 

285 

290 

294 

299 

304 

308 

9 

940 

313 

317 

322 

327 

331 

336 

340 

345 

350 

354 



941 

359 

364 

368 

373 

377 

382 

387 

391 

396 

400 



942 

405 

410 

414 

419 

424 

428 

433 

437 

442 

447 



943 

451 

456 

460 

465 

470 

474 

479 

483 

488 

493 



944 

497 

502 

506 

511 

516 

520 

525 

529 

534 

539 



945 

543 

548 

552 

557 

562 

566 

571 

575 

580 

585 



946 

589 

594 

598 

603 

607 

612 

617 

621 

626 

630 



947 

635 

640 

644 

649 

653 

658 

663 

667 

672 

676 



948 

681 

685 

690 

695 

699 

704 

708 

713 

717 

722 



949 

727 

731 

736 

740 

745 

749 

754 

759 

763 

768 



950 

772 

777 

782 

^786 

791 

795 

800 

804 

809 

813 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 






































VII 


FIVE-PLACE LOGARITHMS OF NUMBERS 


91 


950-1000 


N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

950 

97 772 

777 

"TSf 

786 

791 

795 

800 

804 

809 

813 



951 

818 

823 

827 

832 

836 

841 

845 

850 

855 

859 



952 

864 

868 

873 

877 

882 

886 

891 

896 

900 

905 



953 

909 

914 

918 

923 

928 

932 

937 

941 

946 

950 



954 

955 

959 

964 

968 

973 

978 

982 

987 

991 

996 



955 

98 000 

005 

009 

014 

019 

023 

028 

032 

037 

041 



956 

046 

050 

055 

059 

064 

068 

073 

078 

082 

087 



957 

091 

096 

100 

105 

109 

114 

118 

123 

127 

132 



958 

137 

141 

146 

150 

155 

159 

164 

168 

173 

177 



959 

182 

186 

191 

195 

200 

204 

209 

214 

218 

223 



960 

227 

232 

236 

241 

245 

250 

254 

259 

263 

268 



961 

272 

277 

281 

286 

290 

295 

299 

304 

308 

313 


5 

962 

318 

322 

327 

331 

336 

340 

345 

349 

354 

358 


0.5 

1.0 

1.5 

963 

363 

367 

372 

376 

381 

385 

300 

394 

399 

403 

1 

2 

964 

408 

412 

417 

421 

426 

430 

435 

439 

444 

448 

3 












4 

2.0 

965 

453 

457 

462 

466 

471 

475 

480 

484 

489 

493 

5 

2.5 

966 

498 

502 

507 

511 

516 

520 

525 

529 

534 

538 

6 

3.0 

967 

543 

547 

552 

556 

561 

565 

570 

574 

579 

583 

7 

g 

3.5 

4.0 

4.5 

968 

588 

592 

597 

601 

605 

610 

614 

619 

623 

628 

9 

969 

632 

637 

641 

646 

650 

655 

659 

664 

668 

673 


970 

677 

682 

686 

691 

695 

700 

704 

709 

713 

717 



971 

722 

726 

731 

'776 

735 

740 

744 

749 

753 

758 

762 



972 

767 

771 

780 

784 

789 

793 

798 

802 

807 



973 

811 

816 

820 

825 

829 

834 

838 

843 

847 

851 



974 

856 

860 

865 

869 

874 

878 

883 

887 

892 

896 



975 

900 

905 

909 

914 

918 

923 

927 

932 

936 

941 



976 

945 

949 

954 

958 

963 

967 

972 

976 

981 

985 



977 

989 

994 

998 

*003 

*007 

*012 

*016 

*021 

*025 

*029 



978 

99 034 

038 

043 

047 

052 

056 

061 

065 

069 

074 



979 

078 

083 

087 

092 

096 

100 

105 

109 

114 

118 



980 

123 

127 

131 

136 

140 

145 

149 

154 

158 

162 



981 

167 

171 

176 

180 

185 

189 

193 

198 

202 

207 



982 

211 

216 

220 

224 

229 

233 

238 

242 

247 

251 


4 

983 

255 

260 

264 

269 

273 

277 

282 

286 

291 

295 

1 

2 

0 4 

984 

300 

304 

308 

313 

317 

322 

326 

330 

335 

339 

ois 












3 

1.2 

985 

344 

348 

352 

357 

361 

366 

370 

374 

379 

383 

4 

1.6 

986 

388 

392 

396 

401 

405 

410 

414 

419 

423 

427 

5 

2.0 

2.4 

2 8 

987 

432 

436 

441 

445 

449 

454 

458 

463 

467 

471 

7 

988 

476 

480 

484 

489 

493 

498 

502 

506 

511 

515 

8 

3.2 

989 

520 

524 

528 

533 

537 

542 

546 

550 

555 

559 

9 

3.6 

990 

564 

508 

572 

577 

581 

585 

590 

594 

599 

603 



991 

607 

612 

616 

621 

625 

629 

634 

638 

642 

647 



992 

651 

656 

660 

664 

669 

673 

677 

682 

686 

691 



993 

695 

699 

704 

708 

712 

717 

721 

726 

730 

734 



994 

739 

743 

747 

752 

756 

760 

765 

769 

774 

778 



995 

782 

787 

791 

795 

800 

804 

808 

813 

817 

822 



996 

826 

830 

835 

839 

843 

848 

852 

856 

861 

865 



997 

870 

874 

878 

883 

887 

891 

806 

900 

904 

909 



998 

913 

917 

922 

926 

930 

935 

939 

944 

948 

952 



999 

957 

961 

965 

970 

974 

978 

983 

987 

991 

996 



1000 

00 000 

004 

009 

013 

017 

022 

026 

030 

035 

039 



N 

L 0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

Prop. Pts. 

























































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'X);*^Hr’,‘''‘'','‘‘''.%;: 


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VIII CONSTANTS WITH THEIR LOGARITHMS 93 


Base of Naperian logarithms. 

Modulus of common logarithms .... 

Reciprocal of modulus. 

Circumference of a circle in degrees 
Circumference of a circle in minutes . . . 

Circumference of a circle in seconds . 

Radian expressed in degrees. 

Radian expressed in minutes. 

Radian expressed in seconds. 

Ratio of a circumference to diameter . 

TT = 3.14159 26535 89793 23846 26433 8328 


Number 

e = 2.71828183 
u = 0.43429448 

- = 2.30258509 
u 

= 360 
= 21600 
= 1296000 
= 57.29578 
= 3437.7468 
= 206264.806 
X = 3.14159265 


Logarithm 

0.4342945 

9.6377843-10 


2.5563025 

4.3344538 

6.1126050 

1.7581226 

3.5362739 

5.3144251 

0.4971499 


Number 

2x = 6.28318531 
4x = 12.56637061 
^ = 1.57079633 
\ = 1.04719755 

^ = 4.18879020 

O 

7 = 0.78539816 
4 

7 = 0.52359878 
6 

- = 0.31830989 

X 

— = 0.15915494 
2x 

~ = 0.95492966 
vr 

- = 1.27323954 

X 


Logarithm 

0.7981799 

1.0992099 

0.1961199 

0.0200286 

0.6220886 

9.8950899-10 

9.7189986-10 

9.5028501-10 

9.2018201-10 

9.9799714-10 

0.1049101 


x2 = 9.86960440 

= 0.10132118 
x^ 

Vx = 1.77245385 
= 0.56418958 

Vtt 

I 

a/ - = 0.97720502 

' X 



1 



= 1.12837917 
= 1.46459189 
= 0.68278406 
= 2.14502940 
= 0.62035049 
= 0.80599598 


0.9942997 

9.0057003-10 

0.2485749 

9.7514251-10 

9.9899857-10 

0.0524551 

0.1657166 

9.8342834-10 

0.3314332 

9.7926371-10 

9.9063329-10 


If the radius r = 1, the length of the arc is 

X 


for 1 degree = 
for 1 minute = 
for 1 second = 


180 

X 


10800 

X 

648000 
sin 1" 


= 0.01745329 

= 0.00029089 

= 0.00000485 
= 0.00000485 


8.2418774-10 

6.4637261-10 

4.6855749-10 

4.6855749-10 













TABLE IX 


NATURAL LOGARITHMS OF NUMBERS 
BASE e = 2.71828... 

Note . — Log elO N — Log « N + Log e 10 
N 

Log e — = Log e N - Log c 10 
Log e 10 = 2.30259 

For example : Log ^ 27 = Log e 2.7 + Log e 10 

= 0.99325 + 2.30259 = 3.29584 
Log e .27 = Log p 2.7 — Log p 10 

= 0.99325 - 2.30259 = 8.69066 - 10 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

1.0 

0.0 0000 

0995 

1980 

2956 

3922 

4879 

5827 

6766 

7696 

8618 

1.1 

9531 

*0436 

* 13.33 

*2222 

*3103 

*3976 

*4842 

*5700 

*6551 

*7395 

1.2 

0.1 8232 

9062 

9885 

*0701 

*1511 

*2314 

*3111 

*3902 

*4686 

*5464 

1.3 

0.2 6236 

7003 

7763 

8518 

9267 

*0010 

*0748 

*1481 

*2208 

*2930 

1.4 

0.3 3647 

4359 

5066 

5767 

6464 

7156 

7844 

8526 

9204 

9878 

1.5 

0.4 0547 

1211 

1871 

2527 

3178 

3825 

4469 

5108 

5742 

6373 

1.6 

7000 

7623 

8243 

8858 

9470 

*0078 

*0682 

*1282 

*1879 

*2473 

1.7 

0.5 3063 

3649 

4232 

4812 

5389 

5962 

6531 

7098 

7661 

8222 

1.8 

8779 

9333 

9884 

*0432 

*0977 

*1519 

*2078 

*2594 

*3127 

*3658 

1.9 

0.6 4185 

4710 

5233 

5752 

6269 

6783 

7294 

7803 

8310 

8813 

2.0 

9315 

9813 

*0310 

*0804 

*1295 

*1784 

*2271 

*2755 

*3237 

*3716 

2.1 

0.7 4194 

4669 

5142 

5612 

6081 

6547 

7011 

7473 

7932 

8390 

2.2 

8846 

9299 

9751 

*0200 

*0648 

*1093 

*1536 

*1978 

*2418 

*2855 

2.3 

0.8 3291 

3725 

4157 

4587 

5015 

5442 

5866 

6289 

6710 

7129 

2.4 

7547 

7963 

8377 

8789 

9200 

9609 

*0016 

*0422 

*0826 

*1228 

2.5 

0.9 1629 

2028 

2426 

2822 

3216 

3609 

4001 

4391 

4779 

5166 

2.6 

5551 

5935 

6317 

6698 

7078 

7456 

7833 

8208 

8582 

8954 

2.7 

9325 

9695 

*0063 

*0430 

*0796 

*1160 

*1523 

*1885 

*2245 

*2604 

2.8 

1.0 2962 

3318 

3674 

4028 

4380 

4732 

5082 

5431 

5779 

6126 

2.9 

6471 

6815 

7158 

7500 

7841 

8181 

8519 

8856 

9192 

9527 

3.0 

9861 

*0194 

*0526 

*0856 

*1186 

*1514 

*1841 

*2168 

*2493 

*2817 

3.1 

1.1 3140 

3462 

3783 

4103 

4422 

4740 

5057 

5373 

5688 

6002 

3.2 

6315 

6627 

6938 

7248 

7557 

7865 

8173 

8479 

8784 

9089 

3.3 

9392 

9695 

9996 

*0297 

*0597 

*0896 

*1194 

*1491 

*1788 

*2083 

3.4 

1.2 2378 

2671 

2964 

3256 

3547 

3837 

4127 

4415 

4703 

4990 

3.5 

5276 

5562 

5846 

6130 

6413 

6695 

6976 

7257 

7536 

7815 

3.6 

8093 

8371 

8647 

8923 

9198 

9473 

9746 

*0019 

*0291 

*0563 

3.7 

1.3 0833 

1103 

1372 

1641 

1909 

2176 

2442 

2708 

2972 

3237 

3.8 

3500 

3763 

4025 

4286 

4547 

4807 

5067 

5325 

5584 

5841 

3.9 

6098 

6354 

6609 

6864 

7118 

7372 

7624 

7877 

8128 

8379 

4.0 

8629 

8879 

9128 

9377 

9624 

9872 

*0118 

*0364 

*0610 

*0854 

4.1 

1.4 1099 

1342 

1585 

1828 

2070 

2311 

2552 

2792 

3031 

3270 

4.2 

3508 

3746 

3984 

4220 

4456 

4692 

4927 

5161 

5395 

5629 

4.3 

5862 

6094 

6326 

6557 

6787 

7018 

7247 

7476 

7705 

7933 

4.4 

8160 

8387 

8614 

8840 

9065 

9290 

9515 

9739 

9962 

*0185 

4.5 

1.5 0408 

0630 

0851 

1072 

1293 

1613 

1732 

1951 

2170 

2388 

4.6 

2606 

2823 

3039 

3256 

3471 

3687 

3902 

4116 

4330 

4543 

4.7 

4756 

4969 

5181 

5393 

5604 

5814 

6025 

6235 

6444 

6653 

4.8 

6862 

7070 

7277 

7485 

7691 

7898 

8104 

8309 

8515 

8719 

4.9 

8924 

9127 

9331 

9534 

9737 

9939 

*0141 

*0342 

*0543 

*0744 

5.0 

1.6 0944 

1144 

1343 

1542 

1741 

1939 

2137 

2334 

2531 

2728 

N 

0 

1 

2 

3 

4 

6 

6 

7 

8 

9 


94 






























































































































IX 


FIVE-PLACE NATURAL LOGARITHMS 


95 


N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

5.0 

1.6 0944 

1144 

1343 

1542 

1741 

1939 

2137 

2334 

2531 

2728 

5.1 

2924 

3120 

3315 

3511 

3705 

3900 

4094 

4287 

4481 

4673 

5.2 

4866 

5058 

5250 

5441 

5632 

5823 

6013 

6203 

6393 

6582 

5 . 3 - 

6771 

6959 

7147 

7335 

7523 

7710 

7896 

8083 

8269 

8455 

5.4 

8640 

8825 

9010 

9194 

9378 

9562 

9745 

9928 

*0111 

*0293 

5.5 

1.7 0475 

0656 

0838 

1019 

1199 

1380 

1560 

1740 

1919 

2098 

5.6 

2277 

2455 

2633 

2811 

2988 

3166 

3342 

3519 

3695 

3871 

5.7 

4047 

4222 

4397 

4572 

4746 

4920 

5094 

5267 

5440 

5613 

5.8 

5786 

5958 

6130 

6302 

6473 

6644 

6815 

6985 

7156 

7326 

5.9 

7495 

7665 

7834 

8002 

8171 

8339 

8507 

8675 

8842 

9009 

6.0 

9176 

9342 

9509 

9675 

9840 

*0006 

*0171 

*0336 

*0500 

*0665 

6.1 

1.8 0829 

0993 

1156 

1319 

1482 

1645 

1808 

1970 

2132 

2294 

6.2 

2455 

2616 

2777 

2938 

3098 

3258 

3418 

3578 

3737 

3896 

6.3 

4055 

4214 

4372 

4530 

4688 

4845 

5003 

5160 

5317 

5473 

6.4 

5630 

5786 

5942 

6097 

6253 

6408 

6563 

6718 

6872 

7026 

6.5 

7180 

7334 

7487 

7641 

7794 

*7947 

8099 

8251 

8403 

8555 

6.6 

8707 

8858 

9010 

9160 

9311 

9462 

9612 

9762 

9912 

*0061 

6.7 

1.9 0211 

0360 

0509 

0658 

0806 

0954 

1102 

1250 

1398 

1545 

6.8 

1692 

1839 

1986 

2132 

2279 

2425 

2571 

2716 

2862 

3007 

6.9 

3152 

3297 

3442 

3586 

3730 

3874 

4018 

4162 

4305 

4448 

7.0 

4591 

4734 

4876 

5019 

5161 

5303 

5445 

5586 

5727 

5869 

7.1 

6009 

6150 

6291 

6431 

6571 

6711 

6851 

6991 

7130 

7269 

7.2 

7408 

7547 

7685 

7824 

7962 

8100 

8238 

8376 

8513 

8650 

7.3 

8787 

8924 

9061 

9198 

9334 

9470 

9606 

9742 

9877 

*0013 

7.4 

2.0 0148 

0283 

0418 

0553 

0687 

0821 

0956 

1089 

1223 

1357 

7.5 

1490 

1624 

1757 

1890 

2022 

2155 

2287 

2419 

2551 

2683 

7.6 

2815 

2946 

3078 

3209 

3340 

3471 

3601 

3732 

3862 

3992 

7.7 

4122 

4252 

4381 

4511 

4640 

4769 

4898 

5027 

5156 

5284 

7.8 

5412 

5540 

5668 

5796 

5924 

6051 

6179 

6306 

6433 

6560 

7.9 

6686 

6813 

6939 

7065 

7191 

7317 

7443 

7568 

7694 

7819 

8.0 

7944 

8069 

8194 

8318 

8443 

8567 

8691 

8815 

8939 

9063 

8.1 

9186 

9310 

9433 

9556 

9679 

9802 

9924 

*0047 

*0169 

*0291 

8.2 

2.1 0413 

0535 

0657 

0779 

0900 

1021 

1142 

1263 

1384 

1505 

8.3 

1626 

1746 

1866 

1986 

2106 

2226 

2346 

2465 

2585 

2704 

8.4 

2823 

2942 

3061 

3180 

3298 

3417 

3535 

3653 

3771 

3889 

8.5 

4007 

4124 

4242 

4359 

4476 

4593 

4710 

4827 

4943 

5060 

8.6 

5176 

5292 

5409 

5524 

5640 

5756 

5871 

5987 

6102 

6217 

8.7 

6332 

6447 

6562 

6677 

6791 

6905 

7020 

7134 

7248 

7361 

8.8 

7475 

7589 

7702 

7816 

7929 

8042 

8155 

8267 

8380 

8493 

8.9 

8605 

8717 

8830 

8942 

9054 

9165 

9277 

9389 

9500 

9611 

9.0 

9722 

9834 

9944 

*0055 

*0166 

*0276 

*0387 

*0497 

*0607 

*0717 

9.1 

2.2 0827 

0937 

1047 

1157 

1266 

1375 

1485 

1594 

1703 

1812 

9.2 

1920 

2029 

2138 

2246 

2354 

2462 

2570 

2678 

2786 

2894 

9.3 

3001 

3109 

3216 

3324 

3431 

3538 

3645 

3751 

3858 

3965 

9.4 

4071 

4177 

4284 

4390 

4496 

4601 

4707 

4813 

4918 

5024 

9.5 

5129 

5234 

5339 

5444 

5549 

5654 

5759 

5863 

5968 

6072 

9.6 

6176 

6280 

6384 

6488 

6592 

6696 

6799 

6903 

7006 

7109 

9.7 

7213 

7316 

7419 

7521 

7624 

7727 

7829 

7932 

8034 

8136 

9.8 

8238 

8340 

8442 

8544 

8646 

8747 

8849 

8950 

9051 

9152 

9.9 

9253 

9354 

9455 

9556 

9657 

9757 

9858 

9958 

*0058 

*0158 

10.0 

2.3 0259 

0358 

0458 

0558 

0658 

0757 

0857 

0956 

1055 

1154 

N 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 























































































































































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